Preprint A96/2001
A gap theorem for hypersurfaces of the sphere with constant scalar curvature one
Walcy Santos | Alencar, Hilário | do Carmo, Manfredo
Keywords: scalar curvature | Sphere | Clifford torus | index one
We consider closed hypersurfaces of the sphere with scalar curvature one, prove a gap theorem for a modified second fundamental form and determine the hypersurfaces that are at the end points of the gap. As an application we characterize the index one hypersurfaces with scalar curvature one in the real projective space