A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

Abstract

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F (k) X is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by FX and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that FXS = SFX, where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.