Killing Initial Data on Totally Umbilical & Compact Hypersurfaces
arXiv:0901.3960 · doi:10.1016/j.geomphys.2009.10.001
Abstract
In this note, we give a geometric characterization of the compact and totally umbilical hypersurfaces that carry a non trivial locally static Killing Initial Data (KID). More precisely, such compact hypersurfaces have constant mean curvature and are isometric to one of the following manifolds: (i) Sn the standard sphere, (ii) a finite quotient of a warped product of a circle with a compact Einstein manifold of positive scalar curvature. In particular, these hypersurfaces have harmonic curvature and strictly positive constant scalar curvature.
20 pages, submitted january 2009