In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ...In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.展开更多
In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducin...In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducing 2-parameter loop algebra.展开更多
This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σR,this is a large family of manifolds including the usual space forms R^m,S^m and H^m.We give the fundamental the...This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σR,this is a large family of manifolds including the usual space forms R^m,S^m and H^m.We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σR,which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.展开更多
By using Darboux transformations, the authors give the explicit construction for local iso-metric immersions of space forms Mn(c) into space forms M2n-1(c + ε2) via purely algebraicalgorithm.
In this paper,we obtain a sufficient and necessary condition for a simply connected Riemannian manifold（M^n,g） to be isometrically immersed,as a submanifold with codimension p 〉 1,into the product S^k×H^n＋p＋...In this paper,we obtain a sufficient and necessary condition for a simply connected Riemannian manifold（M^n,g） to be isometrically immersed,as a submanifold with codimension p 〉 1,into the product S^k×H^n＋p＋k of sphere and hyperboloid.展开更多
The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is t...The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is to characterize the anisotropic minimal rotational hypersurfaces in Funk spaces.展开更多
The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ d...The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.展开更多
文摘In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.
基金This work is partially surpported by NNSFC under No. 198111001by the Armored Force Engineering Institute
文摘In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducing 2-parameter loop algebra.
基金Supported by National Natural Science Foundation of China(Grant No.10871149)Doctoral Fund of Education of China(Grant No.200804860046)
文摘This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σR,this is a large family of manifolds including the usual space forms R^m,S^m and H^m.We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σR,which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.
基金Project supported by the National Natural Science Foundation of China (No.10271106)the Science Foundation of the Ministry of Education of Chinathe Natural Science Foundation of Zhejiang Province, China.
文摘By using Darboux transformations, the authors give the explicit construction for local iso-metric immersions of space forms Mn(c) into space forms M2n-1(c + ε2) via purely algebraicalgorithm.
基金Supported by NSFC(Grant Nos.11171091,11371018)partially supported by NSF of He'nan Province(Grant No.132300410141)
文摘In this paper,we obtain a sufficient and necessary condition for a simply connected Riemannian manifold（M^n,g） to be isometrically immersed,as a submanifold with codimension p 〉 1,into the product S^k×H^n＋p＋k of sphere and hyperboloid.
文摘The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is to characterize the anisotropic minimal rotational hypersurfaces in Funk spaces.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region,China(Nos.9041637,CiyuU100711)
文摘The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.
