Abstract
We investigate the differential geometry of spacelike submanifolds of codimension at least two in de Sitter space as an application of the theory of Legendrian singularities. We also discuss related geometric property of spacelike hypersurfaces in de Sitter space. Mathematics Subject Classification (2000): 53A35, 53B30, 58C25.
Highlights
It is known that de Sitter space is a Lorentzian space form with a positive curvature
In [7] we introduced the notion of lightcone Gauss image which is an analogous tool introduced in [3], and investigate the case of spacelike hypersurface in de Sitter space
Fusho and Izumiya [2] firstly introduced the notion of lightlike surface of a spacelike curve in the de Sitter three-space
Summary
It is known that de Sitter space is a Lorentzian space form with a positive curvature. Pei, Romero Fuster and Takahashi [6] introduced the notion of canal hypersurfaces and horospherical hypersurfaces from the normal frames of submanifolds in the hyperbolic space, and investigated submanifolds of higher codimension in the hyperbolic space from the viewpoint of singularity theory. In [7] we introduced the notion of lightcone Gauss image which is an analogous tool introduced in [3], and investigate the case of spacelike hypersurface in de Sitter space. We argue an analogous study of the submanifolds of higher codimension in hyperbolic space [6] and introduce the notions of horospherical hypersurfaces and spacelike canal hypersurfaces by using timelike unit normal vector fields.
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