Bulletin of the Korean Mathematical Society (대한수학회보)

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SEMI-SYMMETRIC STRUCTURE JACOBI OPERATOR FOR REAL HYPERSURFACES IN THE COMPLEX QUADRIC

  • Imsoon Jeong (Department of Mathematics Education Cheongju University) ;
  • Gyu Jong Kim (Department of Mathematics Education Woosuk University) ;
  • Changhwa Woo (Department of Applied Mathematics Pukyong National University)
  • Received : 2022.02.25
  • Accepted : 2023.04.24
  • Published : 2023.07.31
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Abstract

In this paper, we introduce the notion of semi-symmetric structure Jacobi operator for Hopf real hypersufaces in the complex quadric Qm = SOm+2/SOmSO2. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Qm = SOm+2/SOmSO2 with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Qm with either symmetric (parallel), or recurrent structure Jacobi operator.

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Acknowledgement

The first author was supported by grant Proj. No. NRF-2021-R1F1A1064192. The second author was supported by grant by Proj. No. NRF-2020-R1G1A1A-01003570. The third author was supported by grant Proj. No. NRF-2020-R1A2C1A-01101518.

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