Kyungpook Mathematical Journal

  • 제62권1호
  • /
  • Pages.133-166
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  • 2022
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Submanifolds of Codimension 3 in a Complex Space Form with Commuting Structure Jacobi Operator

  • Ki, U-Hang (The National Academy of Sciences) ;
  • Song, Hyunjung (Department of Mathematics Hankuk University of Foreign Studies)
  • 투고 : 2019.11.12
  • 심사 : 2021.02.24
  • 발행 : 2022.03.31
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초록

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form Mn+1(c) for c ≠ 0. We denote by S and R𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R𝜉𝜙 = 𝜙R𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in Mn(c) (⊂ Mn+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

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과제정보

The authors with to express their sincere thanks to the referee who gave us valuable suggestions and comments to improve the paper.

참고문헌

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