Abstract
Abstract
Let M be an orientable connected and compact real hypersurface of the complex space form C
(n + 1)/2. If the mean curvature α and the function f = g(Aξ, ξ) of hypersurface M satisfy the inequality n
2α2 ≤ (n
2 − 1)δ + f
2, where ξ is the characteristic vector field, A is the shape operator and (n − 1)δ is the infimum of the Ricci curvatures of hypersurface M, then it is shown that α is a constant and M is the sphere S
n
(α2) in C
(n + 1)/2.