Killing Initial Data on Totally Umbilical & Compact Hypersurfaces

Details Killing Initial Data on Totally Umbilical & Compact Hypersurfaces Killing Initial Data on Totally Umbilical & Compact Hypersurfaces

2009-01-26

arxiv.org/abs/0901.3960v1

Mathematics

Differential Geometry

20 pages, submitted january 2009

Scientific paper

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.

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