Flat Conformal Structures and the Classification of De Sitter Manifolds

Given a compact n-manifold Σ with a flat conformal structure, there is a canonical procedure for constructing an associated (n + 1)-dimensional de Sitter spacetime homeomorphic to Σ× (0,∞); we call these standard de Sitter spacetimes. Our main theorem is a classification of compact de Sitter manifolds; it asserts that every de Sitter spacetime which is a small regular neighborhood of a closed spacelike hypersurface isometrically embeds in a standard de Sitter spacetime. This complements results of G. Mess in the flat and anti-de Sitter cases.