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The singularities of null surfaces in Anti de Sitter 3-space. (English) Zbl 1185.53017

Summary: 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 space-like 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.

MSC:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
58K60 Deformation of singularities
83C15 Exact solutions to problems in general relativity and gravitational theory
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References:

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