Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A NEW CLASSIFICATION OF REAL HYPERSURFACES WITH REEB PARALLEL STRUCTURE JACOBI OPERATOR IN THE COMPLEX QUADRIC

  • Lee, Hyunjin (Research Institute of Real and Complex Manifolds (RIRCM) Kyungpook National University) ;
  • Suh, Young Jin (Department of Mathematics & RIRCM Kyungpook National University)
  • Received : 2020.06.02
  • Accepted : 2020.10.12
  • Published : 2021.07.01
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Abstract

In this paper, first we introduce the full expression of the Riemannian curvature tensor of a real hypersurface M in the complex quadric Qm from the equation of Gauss and some important formulas for the structure Jacobi operator Rξ and its derivatives ∇Rξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇ξRξ = 0, in the complex quadric Qm for m ≥ 3. In addition, we also consider a new notion of 𝒞-parallel structure Jacobi operator of M and give a nonexistence theorem for Hopf real hypersurfaces with 𝒞-parallel structure Jacobi operator in Qm, for m ≥ 3.

Keywords

Acknowledgement

The first author was supported by grant Proj. No. NRF-2019-R1I1A1A-01050300 and the second author by grant Proj. No. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea.

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