A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

Abstract

A natural codimension one isometric embedding of each -dimensional spherical Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime in the -dimensional Lorentz–Minkowski spacetime permits to contemplate as a rotation Lorentzian hypersurface in . After a detailed study of such Lorentzian hypersurfaces, any k-dimensional spacelike submanifold of such an FLRW spacetime can be contemplated as a spacelike submanifold of . Then, we use that situation to study k-dimensional stationary (i.e. of zero mean curvature vector field) spacelike submanifolds of the FLRW spacetime. In particular, we prove a wide extension of the Lorentzian version of the classical Takahashi theorem, giving a characterization of stationary spacelike submanifolds of when contemplating them as spacelike submanifolds of .