The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an...The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an estimate of the upper bound of the function L(nH)is given,where L is a second-order differential operator.Then,under the assumption that the square norm of the second fundamental form is bounded by a given positive constant,it is proved that Mn must be either totally umbilical or contain two distinct principle curvatures,one of which is simple.Moreover,a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime.Hence,some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case.展开更多
It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is ...It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is a linear combination of Hk+1,…, Hn. This is a new angle to characterize round spheres.展开更多
Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric t...Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.展开更多
We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-...We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.展开更多
基金The Natural Science Foundation of Jiangsu Province(No.BK20161412)the Fundamental Research Funds for the Central Universitiesthe Scientific Innovation Research of College Graduates in Jiangsu Province(No.KYCX17_0041)
文摘The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an estimate of the upper bound of the function L(nH)is given,where L is a second-order differential operator.Then,under the assumption that the square norm of the second fundamental form is bounded by a given positive constant,it is proved that Mn must be either totally umbilical or contain two distinct principle curvatures,one of which is simple.Moreover,a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime.Hence,some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case.
文摘It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is a linear combination of Hk+1,…, Hn. This is a new angle to characterize round spheres.
基金The NNSFC (10371047) and the NSF (04KJD110192) of the Education Department of Jiangsu Province, China.
文摘Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.
基金Li Haizhong is supported by NNSFC No.19701017 Basic Science Research Foundation of Tsinghua University Chen Weihua is supported by NNSFC No.19571005
文摘We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.
