Flat conformal structures and causality in de Sitter manifolds

Our main theorem is a classification of compact de Sitter manifolds, complementing results of G. Mess in the flat and anti-de Sitter cases. The first part of the classification asserts that every de Sitter spacetime which is a small regular neighborhood of a compact spacelike hypersurface isometrically embeds in a standard de Sitter spacetime. This fact is used to obtain our second main result, which states that a compact (2+1)-dimensional de Sitter spacetime with non-empty spacelike boundary is homeomorphic to a product.