2007/07/31 by Patricio S. Letelier
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #astro-ph #gr-qc #math.DG
paper · pdf · doi:10.1007/s10773-007-9565-1
published as Int.J.Theor.Phys.47:1312-1315,2008 · 3 pages, RevTex,small changes, Int. J. Theor. Phys. (in press)
arxiv created 2007/10/01 · openalex publication_date 2007/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For n dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a "detonant" sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel flows. Possible generalizations are mentioned.