Real Hypersurfaces with k-th Generalized Tanaka-Webster Connection in Complex Grassmannians of Rank Two
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In this paper, we consider two kinds of derivatives for the shape operator of areal hypersurface in a Kahler manifold which are named the Lie derivative and the covariantderivative with respect to the k-th generalized Tanaka-Webster connection br(k). Thepurpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of ranktwo, whose Lie derivative of the shape operator coincides with the covariant derivative ofit with respect to br(k) either in direction of any vector eld or in direction of Reeb vectoreld.
Abstract
In this paper, we consider two kinds of derivatives for the shape operator of areal hypersurface in a Kahler manifold which are named the Lie derivative and the covariantderivative with respect to the k-th generalized Tanaka-Webster connection br(k). Thepurpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of ranktwo, whose Lie derivative of the shape operator coincides with the covariant derivative ofit with respect to br(k) either in direction of any vector eld or in direction of Reeb vectoreld.
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