REAL HYPERSURFACES IN A EUCLIDEAN COMPLEX SPACE FORM

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 n²α² ≤ (n² − 1)δ + f², 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 Sⁿ(α²) in C^{(n + 1)/2}.