Lie derivatives and structure Jacobi operator on real hypersurfaces in complex projective spaces

摘要

On a real hypersurface M in a complex projective space we can consider the Levi-Civita connection and for any nonnull constant k the k-th g-Tanaka-Webster connection. Associated to g-Tanaka-Webster connection we can define a differential operator of first order. We classify real hypersurfaces such that both the Lie derivative and this differential operator, either in the direction of the structure vector field xi or in any direction of the maximal holomorphic distribution coincide when we apply them to the structure Jacobi operator of M. (C) 2016 Elsevier B.V. All rights reserved.