Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REAL HYPERSURFACES IN THE COMPLEX HYPERBOLIC QUADRIC WITH CYCLIC PARALLEL STRUCTURE JACOBI OPERATOR

  • Jin Hong Kim (Department of Mathematics Education Chosun University) ;
  • Hyunjin Lee (Department of Mathematics Education Chosun University) ;
  • Young Jin Suh (Department of Mathematics & RIRCM Kyungpook National University)
  • Received : 2023.04.19
  • Accepted : 2023.06.29
  • Published : 2024.03.01
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Abstract

Let M be a real hypersurface in the complex hyperbolic quadric Qm*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator Rξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator Rξ for a real hypersurface M in the complex hyperbolic quadric Qm*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Qm* with such a property.

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Acknowledgement

The authors would like to express their hearty thanks to reviewer for his/her valuable suggestions and comments to develop this article.

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