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Given a compact n-manifold S with a fiat conformal structure, there is a canonical procedure for constructing an associated (n + l)-dimensional de Sitter spacetime homeomorphic to E x (0, oo); 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.

Flat conformal structures and the classification of de Sitter manifolds