Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

Abstract

On a real hypersurface M in a complex two-plane Grassmannian Gz(Cm+z) we have the Lie derivation L and a diòerential operator of order one associated with the generalized Tanaka– Webster connection L(k). We give a classiûcation of real hypersurfaces M on Gz(Cm+z) satisfying L (k) S = L S, where epsilon is the Reeb vector ûeld on M and S the Ricci tensor of M.