Cho Operators on Real Hypersurfaces in Complex Projective Space

Abstract

Let M be a real hypersurface in complex projective space. On M we have the Levi-Civita connection and for any nonzero constant k the corresponding generalized Tanaka-Webster connection. For such a k and any vector field X tangent to M we can define from both connections the kth Cho operator F X (k). We study commutativity properties of these operators with the shape operator and the structure Jacobi operator on M obtaining some characterizations of either Type (A) real hypersurfaces or ruled real hypersurfaces.