Cho Operators on Real Hypersurfaces in Complex Projective Space
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.
KeywordsVector Field Real Hypersurface Shape Operator Complex Projective Space Jacobi Operator
This work was supported by grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea.
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