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

A natural codimension one isometric embedding of each (n+ 1)-dimensional spherical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime I X-f S-n in the (n+ 2)-dimensional Lorentz-Minkowski spacetime Ln+2 permits to contemplate I X-f S-n as a rotation Lorentzian hypersurface in Ln+2. 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 Ln+2. 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 I X-f S-n when contemplating them as spacelike submanifolds of Ln+2.