4 research outputs found
A characterization of quadric constant mean curvature hypersurfaces of spheres
Let be an immersion of a
complete -dimensional oriented manifold. For any , let
us denote by the function given by
and by , the function given by
, where is a Gauss map. We will prove
that if has constant mean curvature, and, for some and some
real number , we have that , then, is
either a totally umbilical sphere or a Clifford hypersurface. As an
application, we will use this result to prove that the weak stability index of
any compact constant mean curvature hypersurface in
which is neither totally umbilical nor a Clifford hypersurface and has constant
scalar curvature is greater than or equal to .Comment: Final version (February 2008). To appear in the Journal of Geometric
Analysi