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