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1.
广义de Sitter空间中的类时超曲面 总被引:1,自引:1,他引:0
利用奇点理论研究广义de Sitter空间中的类时超曲面.介绍类时超曲面的局部微分几何,定义了广义de Sitter高斯像及广义de Sitter高度函数,研究广义deSitter高度函数族的性质及广义de Sitter高斯像的几何意义,介绍了一种证明高度函数为Morse族的新方法.最后研究了类时超曲面的通有性质. 相似文献
2.
In this paper, we will study the golden shaped hypersurfaces in Lorentz space forms. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the golden shaped hypersurfaces in Minkowski space, de Sitter space and anti-de Sitter space, respectively. 相似文献
3.
Oscar M. Perdomo 《Geometriae Dedicata》2011,152(1):183-196
In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space that shows
that this Lorentzian manifold admits algebraic maximal examples of any order. Then, we classify all the space-like order two
algebraic maximal hypersurfaces in the anti de Sitter N-dimensional space. Finally, we provide two families of examples of Lorentzian order two algebraic zero mean curvature hypersurfaces
in the de Sitter space. 相似文献
4.
Masaki Kasedou 《Journal of Geometry》2009,94(1-2):107-121
We define the notions of lightcone Gauss images of spacelike hypersurfaces in de Sitter space. We investigate the relationships between singularities of these maps and geometric properties of spacelike hypersurfaces as an application of the theory of Legendrian singularities. We classify the singularities and give some examples in the generic case in de Sitter 3-space. 相似文献
5.
It is proved that the geometry of lightlike hypersurfaces of the de Sitter space Sn+11 is directly connected with the geometry of hypersurfaces of the conformal space Cn. This connection is applied for a construction of an invariant normalization and an invariant affine connection of lightlike hypersurfaces as well as for studying singularities of lightlike hypersurfaces. 相似文献
6.
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. 相似文献
7.
In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space. 相似文献
8.
We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension two in Minkowski
space, which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local
sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties
of such curvatures and show a Gauss–Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike
hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space. 相似文献
9.
研究了de Sitter空间中具有常数量曲率的类空超曲面,得到了曲面Mn关于截面曲率的一个刚性定理,并且额外获得关于de Sitter空间子流形的一个结论. 相似文献
10.
利用奇点理论研究了广义de Sitter空间中具有Lorentzian法空间的一类超曲面.介绍了这类超曲面的局部微分几何,定义了nullcone Gauss映射及nullcone高度函数族,进而研究了nullcone高度函数族的性质及nullcone高斯映射的几何意义,最后研究了这类超曲面的通有性质. 相似文献
11.
12.
We study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due
to the presence of a closed conformal vector field. More precisely, we begin by extending a result of J. Simons on the minimality
of cones in Euclidean space to these spaces, and apply it to the construction of complete, noncompact minimal Lorentz submanifolds
of both de Sitter and anti-de Sitter spaces. Then we state and prove very general Bernstein-type theorems for spacelike hypersurfaces
in conformally stationary Lorentz manifolds, one of which not assuming the hypersurface to be of constant mean curvature.
Finally, we study the strong r-stability of spacelike hypersurfaces of constant r-th mean curvature in a conformally stationary Lorentz manifold of constant sectional curvature, extending previous results
in the current literature. 相似文献
13.
We study timelike hypersurfaces in anti-de Sitter space from the viewpoint of the Lagrangian/ Legendrian singularity theory. 相似文献
14.
Donghe Pei 《Applicable analysis》2013,92(6):1165-1180
In this paper, we study spacelike submanifolds of codimension two in anti-de Sitter space from the viewpoint of Legendrian singularity theory. We introduce the notion of the anti-de Sitter normalized Gauss map which is a generalization of the ordinary notion of Gauss map of hypersurfaces in Euclidean space. We also introduce the AdS-normalized Gauss–Kronecker curvature for a spacelike submanifold of codimention two in anti-de Sitter space. In the local sense, this curvature describes the contact of submanifolds with some model surfaces. 相似文献
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16.
在文[Classification of type I time-like Hyperspaces with parallel conformal second fundamental forms in the conformal space,Acta Mathematica Sinica,Chinese Series,2011,54(1):125-136]中,我们已对共形空间中具有平行的共形第二基本形式的I型类时超曲面作了分类,本文将探讨其他类型的类时超曲面并完全分类共形空间中具有平行的共形第二基本形式的类时超曲面. 相似文献
17.
开零锥中洛伦兹超曲面的研究难点在于无法利用伪外积运算从切空间中获取该超曲面的法向量.为了解决这一难题,可以借助Legendrian对偶定理的帮助.利用Legendrian对偶定理,构造了开零锥中的Lorentzian超曲面nullcone高斯像,Anti de Sitter高斯像和伪球高斯像并初步建立了开零锥中洛伦兹超曲面的的斜几何. 相似文献
18.
《数学学报(英文版)》2017,(10)
In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space S_1~(m+1) with parallel para-Blaschke tensors. 相似文献
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20.
We consider 3-dimensional anti-de Sitter manifolds with conical singularities along time-like lines, which is what in the
physics literature is known as manifolds with particles. We show that the space of such cone-manifolds is parametrized by
the cotangent bundle of Teichmüller space, and that moreover such cone-manifolds have a canonical foliation by space-like
surfaces. We extend these results to de Sitter and Minkowski cone-manifolds, as well as to some related “quasifuchsian” hyperbolic
manifolds with conical singularities along infinite lines, in this later case under the condition that they contain a minimal
surface with principal curvatures less than 1. In the hyperbolic case the space of such cone-manifolds turns out to be parametrized
by an open subset in the cotangent bundle of Teichmüller space. For all settings, the symplectic form on the moduli space
of 3-manifolds that comes from parameterization by the cotangent bundle of Teichmüller space is the same as the 3-dimensional
gravity one. The proofs use minimal (or maximal, or CMC) surfaces, along with some results of Mess on AdS manifolds, which
are recovered here in a different way, using differential-geometric methods and a result of Labourie on some mappings between
hyperbolic surfaces, that allows an extension to cone-manifolds.
相似文献