共查询到20条相似文献,搜索用时 78 毫秒
1.
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
2.
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
3.
The Lorentzian space form with the positive curvature is called de Sitter space which is an important subject in the theory
of relativity. In this paper we consider spacelike curves in de Sitter 3-space. We define the notion of lightlike surfaces
of spacelike curves in de Sitter 3-space. We investigate the geometric meanings of the singularities of such surfaces.
Work partially supported by Grant-in-Aid for formation of COE. ‘Mathematics of Nonlinear Structure via Singularities’ 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.
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
6.
We give a global conformal representation for flat surfaces with a flat normal bundle in the standard flat Lorentzian space form
4. Particularly, flat surfaces in hyperbolic 3-space, the de Sitter 3-space, the null cone, and other numerous examples aredescribed. 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.
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
9.
Ruled Weingarten surfaces in Minkowski 3-space 总被引:1,自引:0,他引:1
We characterize all ruled surfaces in Minkowski 3-space with a relation between the Gauss and mean curvature (Weingarten surfaces).
It turns out that, except if the rulings are in a null direction, these are given by Lorentzian screw motions of straight
lines. However, if the rulings are always in a null direction, then every ruled surface is Weingarten.
Received: 9 February 1998 / Revised version: 20 December 1998 相似文献
10.
We consider envelopes of one-parameter families of frontals in hyperbolic and de Sitter 2-space from the viewpoint of duality, respectively. Since the classical notions of envelopes for singular curves do not work, we have to find a new method to define the envelope for singular curves in hyperbolic space or de Sitter space. To do that, we first introduce notions of one-parameter families of Legendrian curves by using the Legendrian dualities. Afterwards, we give definitions of envelopes for the one-parameter families of frontals in hyperbolic and de Sitter 2-space, respectively. We investigate properties of the envelopes. At last, we give relationships among those envelopes. 相似文献
11.
Singularities of maximal surfaces 总被引:1,自引:0,他引:1
Shoichi Fujimori Kentaro Saji Masaaki Umehara Kotaro Yamada 《Mathematische Zeitschrift》2008,259(4):827-848
We show that the singularities of spacelike maximal surfaces in Lorentz–Minkowski 3-space generically consist of cuspidal
edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter
3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.
Dedicated to Yusuke Sakane on the occasion of his 60th birthday. 相似文献
12.
Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein’s field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningful to study the submanifold in semi-Euclidean 4-space with index 2. However, the research on the submanifold in semi-Euclidean 4-space with index 2 has not been found from theory of singularity until now. In this paper, as a generalization of the study on lightlike hypersurface in Minkowski space and a preparation for the further study on anti de Sitter space, the singularities of lightlike hypersurface and Lorentzian surface in semi- Euclidean 4-space with index 2 will be studied. To do this, we reveal the relationships between the singularity of distance-squared function and that of lightlike hypersurface. In addition some geometric properties of lightlike hypersurface and Lorentzian surface are studied from geometrical point of view. 相似文献
13.
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
14.
We study the formation of marginally trapped surfaces in the head-on collision of two shock waves in anti-de Sitter space-time.
We compare the obtained results with the corresponding results for de Sitter space-time. To clarify this comparison, we use
coordinates that allow studying AdS/dS cases in a universal way. We also analyze the dependence of the area of the trapped
surface on the choice of the regularization of the shock wave metric. 相似文献
15.
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
16.
Bang-Yen Chen 《Israel Journal of Mathematics》1995,91(1-3):373-391
In [3] the author initiated the study of submanifolds whose mean curvature vectorH is an eigenvector of the Laplacian Δ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type.
The classification of surfaces with ΔH=λH in a Euclidean 3-space was done by the author in 1988. Moreover, in [4] the author classified such submanifolds in hyperbolic
spaces. In this article we study this problem for space-like submanifolds of the Minkowski space-timeE
1
m
when the submanifolds lie in a de Sitter space-time. As a result, we characterize and classify such submanifolds in de Sitter
space-times. 相似文献
17.
Ukrainian Mathematical Journal - We first classify space-like surfaces in the Minkowski space , de Sitter space , and hyperbolic space ?3 with harmonic Gauss maps. Then we characterize and... 相似文献
18.
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
19.
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