2012/05/08 by David N. Pham, Pham, David N.
Mathematics · Physics and Astronomy · #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #math.DG #msc:53C50
paper · pdf · doi:10.48550/arxiv.1205.1702
13 pages, minor revisions
openalex publication_date 2012/05/08 · arxiv created 2012/12/25 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we generalize the defining equation for de Sitter space by replacing the de Sitter radius with a function f satisfying certain conditions; each resulting hypersurface is diffeomorphic to de Sitter space, and has a geometry (and causal character) which is controlled by the choice of f. Necessary and sufficient conditions are obtained for a hypersurface to be timelike, null, or spacelike in the generalized model; in the non-null case, the geometry is given by a warped product. Several examples of timelike, null, and spacelike hypersurfaces are presented. Lastly, we calculate the Ricci tensor and scalar curvature for a special family of 4-dimensional generalized de Sitter spaces.