共查询到20条相似文献,搜索用时 31 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.
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
3.
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
4.
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
5.
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
6.
Sungwook Lee 《Annals of Global Analysis and Geometry》2006,29(4):355-401
It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space ?3 1(?1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in ?SL2? via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E 3 1. The hyperbolic Gauß map of timelike surfaces in ?3 1(?1), which is a close analogue of the classical Gauß map is considered. It is discussed that the hyperbolic Gauß map plays an important role in the study of timelike surfaces of constant mean curvature ± 1 in ?3 1(?1). In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauß map and timelike surface of constant mean curvature ± 1 in ?3 1(?1) is studied. 相似文献
7.
Hong Jianqiao 《数学年刊B辑(英文版)》1995,16(3):361-370
THEGAUSSMAPOFTIMELIKESURFACESINR_1~n¥HONGJIANQIAOAbstract:Gaussmapsoforientedtimelike2-surfacesinarecharacterized,anditisshown... 相似文献
8.
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
9.
10.
Annals of Global Analysis and Geometry - This paper studies timelike minimal surfaces in the De Sitter space $$\mathbb S^3_1(1) \subset \mathbb R^4_1$$ via a complex variable. Using complex... 相似文献
11.
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
12.
Rafael López 《Geometriae Dedicata》1999,76(1):81-95
We prove that a spacelike surface in L3 with nonzero constant mean curvature and foliated by pieces of circles in spacelike planes is a surface of revolution. When the planes containing the circles are timelike or null, examples of nonrotational constant mean curvature surfaces constructed by circles are presented. Finally, we prove that a nonzero constant mean curvature spacelike surface foliated by pieces of circles in parallel planes is a surface of revolution. 相似文献
13.
On any timelike surface with zero mean curvature in the four-dimensional Minkowski space we introduce special geometric (canonical) parameters and prove that the Gauss curvature and the normal curvature of the surface satisfy a system of two natural partial differential equations. Conversely, any two solutions to this system determine a unique (up to a motion) timelike surface with zero mean curvature so that the given parameters are canonical. We find all timelike surfaces with zero mean curvature in the class of rotational surfaces of Moore type. These examples give rise to a one-parameter family of solutions to the system of natural partial differential equations describing timelike surfaces with zero mean curvature. 相似文献
14.
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
15.
In the 3-dimensional de Sitter Space
, a surface is said to be a
spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a
regular curve under the action of the orthogonal transformations of the 4-dimensional
Minkowski space
which leave a timelike (resp. spacelike or degenerate) plane
pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation
surfaces in
. 相似文献
16.
We study timelike hypersurfaces in anti-de Sitter space from the viewpoint of the Lagrangian/ Legendrian singularity theory. 相似文献
17.
We solve the Björling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Björling problems in the Lorentz-Minkowski space. 相似文献
18.
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
19.
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
20.
王红 《纯粹数学与应用数学》1997,(2)
首先通过选取适当的等温参数将三维Minkowski空间R2.1中的全脐点类时曲面与Liouvile方程相联系.其次,通过类时曲面上的类光曲线坐标将R2.1中的类时极值曲面与齐次波动方程相联系.进一步,利用Liouvile方程与齐次波动方程之间的Backlund变换,我们可以从三维Minkowski空间中一个全脐点的类时曲面得到该空间中一个类时极值平移曲面. 相似文献