Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Real Hypersurfaces with k-th Generalized Tanaka-Webster Connection in Complex Grassmannians of Rank Two

  • Jeong, Imsoon (Division of Future Capability Education, Pai Chai University) ;
  • Lee, Hyunjin (The Research Institute of Real and Complex Manifolds (RIRCM), Kyungpook National University)
  • Received : 2017.05.12
  • Accepted : 2017.07.18
  • Published : 2017.10.23
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Abstract

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

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References

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