A note on spacelike submanifolds through light cones in Lorentzian space forms

Abstract

We analyse the intrinsic and extrinsic geometry of spacelike submanifolds in light cones of de Sitter and anti-de Sitter spacetimes by means of an explicit correspondence with the spacelike submanifolds through the light cone in the Lorentz-Minkowski spacetime. In particular, a characterization of totally umbilical compact surfaces through light cones in de Sitter and anti-de Sitter is shown and we obtain an estimation of the rst eigenvalue of the Laplace operator on a compact spacelike surface in a light cone