Spacelike submanifolds of codimension two in anti-de Sitter space

ABSTRACT

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.

KEYWORDS:

• Anti-de Sitter space
• AdS-nomalized Gauss map
• lightlike hypersurface
• AdS-hyperhorosphere

AMS SUBJECT CLASSIFICATIONS:

• 53A35
• 53B20
• 57R45

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NSFC of China [grant number 11271063] and [grant number 11671070].