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

초록

The almost contact metric structure that we have on a real hypersurface M in the complex quadric Q(m) = SOm+2/SOmSO2 allows us to define, for any nonnull real number k, the k-th generalized Tanaka-Webster connection on M, del(<^>(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 Q(m) for which any of those tensors identically vanishes, in the particular case of B being the structure Lie operator L-xi on M.

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