East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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STRUCTURE JACOBI OPERATORS AND REAL HYPERSURFACES OF TYPE(A) IN COMPLEX SPACE FORMS

  • Received : 2020.09.17
  • Accepted : 2020.11.26
  • Published : 2021.01.31
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Abstract

Let M be a real hypersurface with almost contact metric structure (��, ξ, ��, g) in a nonflat complex space form Mn(c). We denote S and Rξ by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field ξ respectively. In this paper, we prove that M is a Hopf hypersurface of type (A) in Mn(c) if it satisfies Rξ�� = ��Rξ and at the same time satisfies $({\nabla}_{{\phi}{\nabla}_{\xi}{\xi}}R_{\xi}){\xi}=0$ or Rξ��S = S��Rξ.

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References

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