局部对称Lorentz空间中的具有常数量曲率的完备类空超曲面

The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L_1 introduced by S Y Cheng and S T Yau [3].     

Linear Weingarten Spacelike Submanifolds in Semi-Riemannian Space Form

Mathematical Notes - We consider the linear Weingarten spacelike submanifold immersed in semi-Riemannian space form $$mathbb {N}^{n+p} _q (c)$$ of constant sectional curvature $$c$$ and index...     

局部对称流形中具常平均曲率的完备超曲面

本文研究了局部对称流形中具常平均曲率的完备超曲面，得到了这种超曲面的一个特征定理，推广了H．Alencar和M．do Carmo以及N．X．Shui和G．Q．Wu的结果。     

On the Curvatures of Complete Spacelike Hypersurfaces in de Sitter Space

We establish some estimates for the higher-order mean curvatures, the scalar curvature and the Ricci curvature of a complete spacelike hypersurface in de Sitter space which is contained in certain unbounded regions of the ambient space. Our results will be an application of a generalized maximum principle due to Omori.     

Totally Umbilical Hypersurfaces in a Locally Symmetric Manifold

In this paper we obtain some formulas for totally umbilical hypersurfaces in a locally symmetric manifold, and derive some local results on the hypersurfaces from these formulas.     

Spacelike Mobius Hypersurfaces in Four Dimensional Lorentzian Space Form

In this paper, we first set up an alternative fundamental theory of M?bius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {E_i}. Then we give a complete classification for spacelike M?bius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either M?bius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing M?bius form.     

On the Unicity of Complete Hypersurfaces Immersed in a Semi-Riemannian Warped Product

Our purpose is to apply appropriate generalized maximum principles in order to study the unicity of complete hypersurfaces immersed in a semi-Riemannian warped product, which is supposed to obey a suitable convergence condition. In this setting, by assuming a natural comparison inequality between the r-th mean curvatures of the hypersurface and the ones of the slices of the slab where the hypersurface is contained, we establish sufficient conditions to guarantee that such a hypersurface must be a slice.     

Locally Symmetric Connections on Complex Hypersurfaces with Type Number 1

We characterize – by describing in local coordinates their sections – the transversal bundles which on the complex hypersurface with type number 1 induce locally symmetric connections.     

Lorentz空间型中具有常数量曲率类空超曲面

研究了Lorentz空间型中具有常数量曲率的紧致类空超曲面,得到了这类超曲面的内蕴刚性定理.     

Minimal Submanifolds in a Locally Symmetric and Conformally Flat Space

We study minimal submanifolds in the locally symmetric and conformally flat Riemannian manifold and generalize Yau's result obtained in J. Amer. Math. 97 (1975), 76–100.     

关于局部对称空间中2-调和子流形

本文研究局部对称完备黎曼流形中的紧致2－调和子流形，得到了这类流形第二基本模式长平方的Pinching定理及推广的J．Simons型积分不等式。     

Hypersurfaces of a Lorentz space form

The project supported by NNSFC, FECC and CPF.     

Complete Hypersurfaces with Two Distinct Principal Curvatures in a Space Form

Results in Mathematics - In this paper, we study complete hypersurfaces M n immersed in a space form $${\mathbb{Q}_c^{n+1}}$$ , with $${c \in \{-1,0,1\}}$$ and $${n \geq 2}$$ , having two distinct...     

Time-like Linear Weingarten Surfaces in Lorentzian Space Forms

In this paper we study Backlund transformations of time-like linear Weingarten surfaces with negative discriminant in Lorentzian space forms.     

局部完备局部凸空间中的向量值变分原理

给出了局部完备局部凸空间中的向量值Ekeland变分原理,并以次可加、严格增的连续函数作为扰动.     

Curvature Flow of Complete Convex Hypersurfaces in Hyperbolic Space

We investigate the existence, convergence, and uniqueness of modified general curvature flow (MGCF) of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.     

de Sitter空间中具平行平均曲率向量的完备类空子流形(Ⅱ)

本文证明了de Sitter空间中具平行平均曲率向量的完备类空子流形在其第二基本形式模长平方S＜2(n-1c)的平方根时是全脐子流形。     

在Sn1+1空间中具有常数量曲率的类空超曲面的高斯映射

在这篇文章中,我们研究在de Sitter空间中具有非负常值的第r个平均曲率的紧致的类空超曲面.我们证明了在合适的条件下紧致的类空超曲面是全脐的.     

Minkowski空间中带超平面边界的紧致类空超曲面

In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients.     

Complete Minimal Hypersurfaces in a Sphere

In this paper we investigate complete minimal hypersurfaces with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mⁿ) is a minimal Clifford torus.