In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operato...In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.展开更多
We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found ...We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.展开更多
A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the sla...A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.展开更多
For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are ...For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.展开更多
Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compac...Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.展开更多
Let f: Mn(?)Sn+1 C Rn+2 be an n-dimensional complete oriented Rieman-nian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by S_+~n+1 the upper closed hemisphere. If f(Mn)(?)_+~n+1, then un...Let f: Mn(?)Sn+1 C Rn+2 be an n-dimensional complete oriented Rieman-nian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by S_+~n+1 the upper closed hemisphere. If f(Mn)(?)_+~n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature.展开更多
We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck form...We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.展开更多
In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the...In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.展开更多
In this paper,we study the stability of the domains in a surface of constant meam curvaturein space form N3(c)by means of the estimation of the Gaussian curvature of comformal metric onthis surface.
In this paper, we obtain Chen＇s inequalities for totally real submanifolds in complex space forms with a semi-symmetric metric connection. Also, some results of A. Mihai and C. Ozgiir＇s paper have been modified.
In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, propo...In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, proposed the methods for integrating and optimizing campus spaces, such as establishing artistic conception of campus space, improving campus traffic organization, creating and improving the external communication spaces, on the basis of analyzing evolution history of campus spaces.展开更多
By using the methods introduced by Chen[Chen Bang-yen,A series of Ka¨hlerian invarianrts and their applications to Khlerian geometry,Beitrge Algebra Geom,2001,42(1):165-178],we establish some inequalities for...By using the methods introduced by Chen[Chen Bang-yen,A series of Ka¨hlerian invarianrts and their applications to Khlerian geometry,Beitrge Algebra Geom,2001,42(1):165-178],we establish some inequalities for invariant submanifolds in a Sasakian space form involving totally real sectional curvature and the scalar curvature.Moreover,we consider the case of equalities.展开更多
In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src=&...In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of L<sup>p</sup> p-harmonic 1-forms on M<sup>m</sup>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.展开更多
Some new intrinsic rigidity theorems of minimal integral submanifolds in a sasaki space form are obtained, so the corresponding results due to Maeda and Qu are improved.
In this paper, we firstly give a general inequality for the lower order eigenvalues of elliptic operators in weighted divergence form on compact smooth metric measure spaces with boundary（possibly empty）. Then using...In this paper, we firstly give a general inequality for the lower order eigenvalues of elliptic operators in weighted divergence form on compact smooth metric measure spaces with boundary（possibly empty）. Then using this general inequality, we get some universal inequalities for the lower order eigenvalues of elliptic operators in weighted divergence form on a connected bounded domain in the smooth metric measure spaces.展开更多
In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finall...In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.展开更多
In order to explore the interaction effects of line spacing and seedling belt width on wheat yield formation and improve the cultivation techniques of broadwidth and fine seeding of wheat,a high-yielding winter wheat ...In order to explore the interaction effects of line spacing and seedling belt width on wheat yield formation and improve the cultivation techniques of broadwidth and fine seeding of wheat,a high-yielding winter wheat cultivar Shannong 28 was selected as material. Using the split plot design,the main plot was set with line spacing as 20,25 and 30 cm,respectively,and the sub-plot was set with seedling belt width as 3,5,7,9 and 11 cm,respectively. Then,the population dynamics,dry matter accumulation and translocation and yield of wheat were studied under the experimental conditions. The results showed that under the line spacing of 20 cm,the dry matter accumulation and yield of winter wheat were higher with the seedling belt width of 5 cm. When the line spacing was 25 cm,the dry matter accumulation and yield under the seedling belt width of 9 cm reached a high level. Under the line spacing of 30 cm,Shannong 28 achieved higher dry matter accumulation and yield with the seedling belt width of 11 cm. Comprehensive analysis revealed that the suitable treatment for Shannong 28 was 25 cm of line spacing with 9 cm of seedling belt width,which could realize the coordination of the three factors of yield composition and get higher yield. Therefore,the reasonable line spacing and seedling belt width were the important technical ways to realize high yield of wheat.展开更多
By exploring the space and the design techniques of roof garden in Frank Gehry's Walt Disney Concert Hall, this paper made further research on the combination of architectural functions and pedestrian fl ow lines,...By exploring the space and the design techniques of roof garden in Frank Gehry's Walt Disney Concert Hall, this paper made further research on the combination of architectural functions and pedestrian fl ow lines, and attempted to summarize the unique design techniques of Frank Gehry by analyzing his works, improve and develop design theories of roof garden, and attract more attention from the public to roof garden design.展开更多
We have discussed the C-totally real subrnanifolds with parallel mean curvature vector of Sasakian space form, obtained a formula of J.Simons type, and improved one result of S.Yamaguchi.
In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
基金Supported by National Natural Science Foundation of China(12161078)Foundation for Innovative Fundamental Research Group Project of Gansu Province(24JRRA778)Project of Northwest Normal University(20240010)。
文摘In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.
基金Supported by the Ministry of Education and Science of Ukraine under Grant No 0117U002253
文摘We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.
基金This project is supported by the NSFC(10271041)Tianyuan Youth Foundation of Mathematics.
文摘A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.
基金Supported by the Natural Science Foundation of Henan(004051900)
文摘For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.
文摘Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.
文摘Let f: Mn(?)Sn+1 C Rn+2 be an n-dimensional complete oriented Rieman-nian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by S_+~n+1 the upper closed hemisphere. If f(Mn)(?)_+~n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature.
基金supported by the Foundation for training Young Teachers in University of Shanghai(ZZegd16003)supported by National Natural Science Foundation of China(11271071,11771087)LMNS,Fudan University
文摘We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.
文摘In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.
基金Supported by N.NSF of China(19871038)Supported by the NSF of Jiangxi(981105)
文摘In this paper,we study the stability of the domains in a surface of constant meam curvaturein space form N3(c)by means of the estimation of the Gaussian curvature of comformal metric onthis surface.
基金the Foundation for Excellent Young Talents of Higher Education of Anhui Province(GrantNo.2011SQRL021ZD)
文摘In this paper, we obtain Chen＇s inequalities for totally real submanifolds in complex space forms with a semi-symmetric metric connection. Also, some results of A. Mihai and C. Ozgiir＇s paper have been modified.
基金Sponsored by Humanities and Social Sciences Program of Jiangxi Universities and Colleges(JC1434)The"Twelfth Five-year Plan"(2014)Program of Jiangxi Provincial Social Sciences(14SH05)Program of Jiangxi Provincial Arts and Scientifi c Planning(YG2014113)
文摘In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, proposed the methods for integrating and optimizing campus spaces, such as establishing artistic conception of campus space, improving campus traffic organization, creating and improving the external communication spaces, on the basis of analyzing evolution history of campus spaces.
基金Supported by the NSFC of China(11001076)Supported by the NSF of Henan Provincial Education Department(2010A110008)
文摘By using the methods introduced by Chen[Chen Bang-yen,A series of Ka¨hlerian invarianrts and their applications to Khlerian geometry,Beitrge Algebra Geom,2001,42(1):165-178],we establish some inequalities for invariant submanifolds in a Sasakian space form involving totally real sectional curvature and the scalar curvature.Moreover,we consider the case of equalities.
文摘In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of L<sup>p</sup> p-harmonic 1-forms on M<sup>m</sup>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
文摘Some new intrinsic rigidity theorems of minimal integral submanifolds in a sasaki space form are obtained, so the corresponding results due to Maeda and Qu are improved.
基金Supported by the National Natural Science Foundation of China(Grant No.11401131)the Natural Science Foundation of Hubei Provincial Department of Education(Grant No.Q20154301)
文摘In this paper, we firstly give a general inequality for the lower order eigenvalues of elliptic operators in weighted divergence form on compact smooth metric measure spaces with boundary（possibly empty）. Then using this general inequality, we get some universal inequalities for the lower order eigenvalues of elliptic operators in weighted divergence form on a connected bounded domain in the smooth metric measure spaces.
文摘In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
基金Supported by National Key R&D Program of China (2017YFD0301001)Shandong Province Modern Agricultural Technology Wheat Innovation Team (SDAIT-04-022+1 种基金SDAIT-01-08)Agricultural Scientific and Technological Innovation project of Shandong Academy of Agricultural Sciences (CXGC2016B01)。
文摘In order to explore the interaction effects of line spacing and seedling belt width on wheat yield formation and improve the cultivation techniques of broadwidth and fine seeding of wheat,a high-yielding winter wheat cultivar Shannong 28 was selected as material. Using the split plot design,the main plot was set with line spacing as 20,25 and 30 cm,respectively,and the sub-plot was set with seedling belt width as 3,5,7,9 and 11 cm,respectively. Then,the population dynamics,dry matter accumulation and translocation and yield of wheat were studied under the experimental conditions. The results showed that under the line spacing of 20 cm,the dry matter accumulation and yield of winter wheat were higher with the seedling belt width of 5 cm. When the line spacing was 25 cm,the dry matter accumulation and yield under the seedling belt width of 9 cm reached a high level. Under the line spacing of 30 cm,Shannong 28 achieved higher dry matter accumulation and yield with the seedling belt width of 11 cm. Comprehensive analysis revealed that the suitable treatment for Shannong 28 was 25 cm of line spacing with 9 cm of seedling belt width,which could realize the coordination of the three factors of yield composition and get higher yield. Therefore,the reasonable line spacing and seedling belt width were the important technical ways to realize high yield of wheat.
文摘By exploring the space and the design techniques of roof garden in Frank Gehry's Walt Disney Concert Hall, this paper made further research on the combination of architectural functions and pedestrian fl ow lines, and attempted to summarize the unique design techniques of Frank Gehry by analyzing his works, improve and develop design theories of roof garden, and attract more attention from the public to roof garden design.
文摘We have discussed the C-totally real subrnanifolds with parallel mean curvature vector of Sasakian space form, obtained a formula of J.Simons type, and improved one result of S.Yamaguchi.
文摘In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
