共查询到20条相似文献,搜索用时 15 毫秒
1.
We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory. 相似文献
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从切触几何及Legendrian奇点理论的角度研究了广义de sitter空间中的类时超曲面的切触性质及gdS-高斯像的奇点的分类和几何意义. 相似文献
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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
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Liang Chen Qixing Han Weizhi Sun 《Journal of Mathematical Analysis and Applications》2010,366(1):256-265
We study the geometric properties of degenerate surfaces, which are called AdS null surfaces, in Anti de Sitter 3-space from a contact viewpoint. These surfaces are associated to spacelike curves in Anti de Sitter 3-space. We define a map which is called the torus Gauss image. We also define two families of functions and use them to investigate the singularities of AdS null surfaces and torus Gauss images as applications of singularity theory of functions. 相似文献
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作为R_(2~4)空间中子流形研究的补充工作,试图利用Lagrange奇点理论对R_(2~4)空间中三维Lorentzian子流形的微分几何性质及奇异性进行研究. 相似文献
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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 non negative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥1. When 2(n-1)~(1.2)/n < H < 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder. 相似文献
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Juan A. Aledo Luis J. Alí as 《Proceedings of the American Mathematical Society》2002,130(4):1145-1151
In this paper we prove that a complete spacelike hypersurface in de Sitter space such that its image under the Gauss map is contained in a hyperbolic geodesic ball of radius is necessarily compact and its -dimensional volume satisfies , where denotes the volume of a unitary round -sphere. We also characterize the case where these inequalities become equalities. As an application of our result, we also conclude that Goddard's conjecture is true under the assumption that the hyperbolic image of the hypersurface is bounded.
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In this paper we prove an integral inequality for the Gaussian curvature of compact maximal surfaces inn-dimensional de Sitter space. Some applications of that inequality are given in order to solve the associated Bernstein type problem as well as to characterize the totally geodesic immersion in terms of its area and the first nontrivial eigenvalue of its Laplacian.Partially supported by a DGICYT Grant No. PB91-0705-C02-02Partially supported by a DGICYT Grant No. PB91-0731 相似文献
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A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13. 相似文献
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设M是常曲率c的de Sitter空间S1^n+1(c)的常平均曲率的完备类空超曲面,S表示第二形式的范数平方。本文证明:差S〈2√n-1c,则M是全脐的和等距于一球面。 相似文献
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研究了deSitter空间中具有常数量曲率的类空子流形,利用活动标架的方法,证明了这类子流形的某些刚性定理,推广了已有的一些结果. 相似文献
14.
Luis J. Alías 《Geometriae Dedicata》1999,77(3):297-304
In this paper we establish a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a pinching condition for the Ricci curvature. Our result will be a consequence of an integral formula involving the Ricci curvature and the scalar curvature of the hypersurface. We also derive some other consequences and applications of this formula. 相似文献
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CompleteSpace-likeSubmanifoldsinadeSitterSpacewithParallelMeanCurvatureVectorShuShichang(XianyangTeachersCollege,Xianyang,712... 相似文献
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We study the singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space through their contact with hyperplanes. 相似文献
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We prove the existence of a global in time solution of the semilinear Klein–Gordon equation in the de Sitter space–time. The coefficients of the equation depend on spatial variables as well, that make results applicable to the space–time with the time slices being Riemannian manifolds. 相似文献
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de Sitter空间中具平行平均曲率向量的完备类空子流形 总被引:3,自引:0,他引:3
本文证明了deSitter空间中具平行平均曲率向量的完备类空子流形在H2〉C时其第二基本形式模长平方是上有界的,从而推广了U-HangKI^(4)及Q.M.Cheng^(3)中的结果。 相似文献
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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。 相似文献