HYPERSURFACES OF S^(n+1) WITH TWO DISTINCT PRINCIPAL CURVATURES

The aim of this paper is to prove that the Ricci curvature Ric(M) of a complete hypersurface M^n, n=>3, of the Euclidean sphere S^(n+1), with two distinct principal curvatures of multiplicity 1 and n-1, satisfies Ric(M) => inf f(H), for a function\, f depending only on n and the mean curvature H. Supposing in addition that M^n is compact, we will show that the equality occurs if and only if H is constant and M^n is isometric to a Clifford torus S^(n-1)(r) * S^1(radical(1-r^2)).