Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Structure Jacobi Operators of Real Hypersurfaces with Constant Mean Curvature in a Complex Space Form

  • Received : 2016.02.08
  • Accepted : 2016.07.11
  • Published : 2016.12.23
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Abstract

Let M be a real hypersurface with constant mean curvature in a complex space form $M_n(c),c{\neq}0$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ with respect to the structure vector field ${\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor field ${\phi}$, then M is a homogeneous real hypersurface of Type A.

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References

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