2008/03/31 by Ali Ulaş Özgür Kişisel, Ali Ulas Ozgur Kisisel, Özgür Sarıoğlu +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Conformal map #Curvature #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometric flow #Geometry #Geometry and complex manifolds #Hele-Shaw flow #Homogeneous #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Open-channel flow #Physics #Pure mathematics #Ricci curvature #Ricci flow #Scalar curvature #Statistical physics #Yamabe flow #gr-qc #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1088/0264-9381/25/16/165019
published as Class.Quant.Grav.25:165019,2008 · 17 pages, 4 figures, exact solutions of two geometries given, exposition of several parts expanded, references updated
arxiv created 2008/06/17 · openalex publication_date 2008/08/05 · arxiv updated 2009/12/01 · openalex created_date 2020/07/02 · openalex updated_date 2026/08/05
Using the conformally-invariant Cotton tensor, we define a geometric flow, the Cotton flow , which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an entropy functional, and study the flow of nine homogeneous spaces both numerically and analytically. In particular, we show that the arbitrarily deformed homogeneous 3-sphere flows into the round 3-sphere. Two of the nine homogeneous geometries, which are degenerated by the Ricci flow, are left intact by the Cotton flow.