In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkow...In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.展开更多
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like subm...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.展开更多
In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz ...In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2).展开更多
In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian cu...In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.展开更多
This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal sur...This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.展开更多
We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on ...We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).展开更多
文摘In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.
基金Supported by the Education Commission of Henan Province(20021100002) Supported by the NSF of Henan University(200110475028)
文摘In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2).
基金supported by the NSFC (11071248, 11071249)supported by the Fundamental Research Funds for the Central Universities(USTC)
文摘In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.
基金Supported by the National Natural Science Fundation of China.
文摘This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11871450).
文摘We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).
