A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms - George Kaimakamis; Konstantina Panagiotidou; Juan de Dios Pérez (Mathematics, 2020)
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 <semantics> <msubsup> F X ( k ) </msubsup> </semantics> is defined and is related to both connections. If X belongs to the maximal holomorphic distribution <semantics> D </semantics> on M, the corresponding operator does not depend on k and is denoted by <semantics> F X </semantics> and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that <semantics> F X S = S F X </semantics> , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.