共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):156-173
We define the notions of (S
t
1 × S
s
2)-nullcone Legendrian Gauss maps and S
+2-nullcone Lagrangian Gauss maps on spacelike surfaces in anti de Sitter 4-space. We investigate the relationships between
singularities of these maps and geometric properties of surfaces as an application of the theory of Legendrian/Lagrangian
singularities. By using S
+2-nullcone Lagrangian Gauss maps, we define the notion of S
+2-nullcone Gauss-Kronecker curvatures and show a Gauss-Bonnet type theorem as a global property. We also introduce the notion
of horospherical Gauss maps which have geometric properties different from those of the above Gauss maps. As a consequence,
we can say that anti de Sitter space has much richer geometric properties than the other space forms such as Euclidean space,
hyperbolic space, Lorentz-Minkowski space and de Sitter space. 相似文献
3.
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
4.
Qiyu Chen Jean-Marc Schlenker 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(1):181-216
We prove that any 3-dimensional hyperbolic end with particles (cone singularities along infinite curves of angles less than π) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with particles and convex globally hyperbolic maximal (GHM) de Sitter spacetime with particles, it follows that any 3-dimensional convex GHM de Sitter spacetime with particles also admits a unique foliation by constant Gauss curvature surfaces. We prove that the grafting map from the product of Teichmüller space with the space of measured laminations to the space of complex projective structures is a homeomorphism for surfaces with cone singularities of angles less than π, as well as an analogue when grafting is replaced by “smooth grafting”. 相似文献
5.
This paper considers the one parameter families of extrinsic differential geometries of Lorentzian hypersurfaces on pseudo n‐spheres. We give a continuous relationship among the three types Gauss indicatrices by one parameter map. Meanwhile, we also give the singularity analysis of the one parameter Gauss indicatrices of Lorentzian hypersurfaces on pseudo n‐spheres by the Legendrian singularity theory. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
We study timelike surfaces in Anti de Sitter 3-space as an application of singularity theory. We define two mappings associated
to a timelike surface which are called Anti de Sitter nullcone Gauss image and Anti de Sitter torus Gauss map. We also define a family of functions named Anti de Sitter null height function on the timelike surface. We use this family of functions as a basic tool to investigate the geometric meanings of singularities
of the Anti de Sitter nullcone Gauss image and the Anti de Sitter torus Gauss map. 相似文献
7.
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
8.
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
9.
主要通过定义在指标数为2的5维伪欧氏空间中的3维类时子流形M上的类时高斯映射和类时高度函数,并研究M与管状超曲面CM的奇点分类. 相似文献
10.
Singularities of Hyperbolic Gauss Maps 总被引:1,自引:0,他引:1
Izumiya Shyuichi; Pei Donghe; Sano Takasi 《Proceedings London Mathematical Society》2003,86(2):485-512
In this paper we adopt the hyperboloid in Minkowski space asthe model of hyperbolic space. We define the hyperbolic Gaussmap and the hyperbolic Gauss indicatrix of a hypersurface inhyperbolic space. The hyperbolic Gauss map has been introducedby Ch. Epstein [J. Reine Angew. Math. 372 (1986) 96135]in the Poincaré ball model, which is very useful forthe study of constant mean curvature surfaces. However, it isvery hard to perform the calculation because it has an intrinsicform. Here, we give an extrinsic definition and we study thesingularities. In the study of the singularities of the hyperbolicGauss map (indicatrix), we find that the hyperbolic Gauss indicatrixis much easier to calculate. We introduce the notion of hyperbolicGaussKronecker curvature whose zero sets correspond tothe singular set of the hyperbolic Gauss map (indicatrix). Wealso develop a local differential geometry of hypersurfacesconcerning their contact with hyperhorospheres. 2000 MathematicalSubject Classification: 53A25, 53A05, 58C27. 相似文献
11.
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
12.
Ben McCarty 《Topology and its Applications》2012,159(1):162-174
For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. 相似文献
13.
Izumiya S.; Pei D.; Fuster M. C. Romero; Takahashi M. 《Journal London Mathematical Society》2005,71(3):779-800
Some geometrical properties associated to the contact of submanifoldswith hyperhorospheres in hyperbolic n-space are studied as anapplication of the theory of Legendrian singularities. 相似文献
14.
We study real minimal surfaces : M2 4 under the hypothesisthat the holomorphic Gauss map of the immersion is invariantby a holomorphic foliation with singularities. We give a sortof HuberOsserman theorem regarding the algebraicity ofthe holomorphic Gauss map. 相似文献
15.
Donghe Pei Lingling Kong Jianguo Sun Qi Wang 《Journal of Mathematical Analysis and Applications》2012,385(1):243-253
The main goal of this paper is to study singularities of lightlike torus Gauss maps of Lorentzian surfaces (i.e., both tangent plane and normal plane are Lorentz) in semi-Euclidean 4-space with index 2. To do this, we construct a Lorentzian lightlike torus height function and reveal relations between singularities of the Lorentzian lightlike torus height function and those of lightlike torus Gauss map. In addition we study some properties of Lorentzian surface from geometrical viewpoint. 相似文献
16.
Vladimir Tchernov 《Topology》2003,42(1):1-33
We show that for a large class of contact three-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's J+-type invariants of wave fronts on a surface F is isomorphic to the group of Vassiliev invariants of framed knots in the spherical cotangent bundle ST∗F of F.On the other hand, we construct the first examples of contact manifolds for which Vassiliev invariants of Legendrian knots can distinguish Legendrian knots that realize isotopic framed knots and are homotopic as Legendrian immersions. 相似文献
17.
We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic p. In particular, it is shown that any variety in p>0 has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if p=2. 相似文献
18.
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
19.
We use minimal Legendrian submanifolds in spheres to construct examples of absolutely area-minimizing cones and we prove a result about Legendrian 2-tori in S5. 相似文献
20.
Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds
Hajime Ono 《Differential Geometry and its Applications》2005,22(3):327-340
First, we derive a new second variation formula which holds for minimal Legendrian submanifolds in Sasakian manifolds. Using this, we prove that any minimal Legendrian submanifold in an η-Einstein Sasakian manifold with “nonpositive” η-Ricci constant is stable. Next we introduce the notion of the Legendrian stability of minimal Legendrian submanifolds in Sasakian manifolds. Using our second variation formula, we find a general criterion for the Legendrian stability of minimal Legendrian submanifolds in η-Einstein Sasakian manifolds with “positive” η-Ricci constant. 相似文献