KILLING INITIAL DATA ON TOTALLY UMBILICAL & COMPACT HYPERSURFACES

Daniel Maerten (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: Scalar curvature; harmonic curvature; Einstein metrics; Schwarzschild–de Sitter metrics; constraints application; Lafontaine equation.; Lafontaine equation

Domaines: Géométrie différentielle [math.DG]

Daniel Maerten. KILLING INITIAL DATA ON TOTALLY UMBILICAL & COMPACT HYPERSURFACES. 2009. ⟨hal-00355882⟩