A note on hypersurfaces in a Euclidean space (Q913281)

The object of this note is to prove the following theorem: Let M be a complete and connected hypersurface of \(R^{n+1}\). If the Ricci curvature of M satisfies \(Ric(X,X)\geq (n-1)\| h(X,X)\|^ 2\) for any unit vector field X on M, then M is either a hyperplane or a sphere. This result is achieved by considering the Laplacian of the second fundamental form h as a function on the unit normal bundle.