On the Structure Lie Operator of a Real Hypersurface in the Complex Quadric

Abstract

ABSTRACT The almost contact metric structure that we have on a real hypersurface M in the complex quadric Qm = SO m+2/SO m SO 2 allows us to define, for any nonnull real number k, the k-th generalized Tanaka-Webster connection on M, ∇ ^ ( k ) . Associated to this connection, we have Cho and torsion operators F X ( k ) and T X ( k ) , respectively, for any vector field X tangent to M. From them and for any symmetric operator B on M, we can consider two tensor fields of type (1,2) on M that we denote by B F ( k ) and B T ( k ) , respectively. We classify real hypersurfaces M in Qm for which any of those tensors identically vanishes, in the particular case of B being the structure Lie operator Lξ on M.