Flat conformal structures and the classification of de Sitter manifolds
Published in Communications in Analysis and Geometry, 1999
Recommended citation: Kevin P. Scannell. Flat conformal structures and the classification of de Sitter manifolds. Communications in Analysis and Geometry, 7(2):325–345, 1999. https://kevinscannell.com/files/cag.pdf
DOI: doi:10.4310/CAG.1999.v7.n2.a6
Abstract: 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.