• 제목/요약/키워드: distingushed normal vector

검색결과 1건 처리시간 0.013초

SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN A COMPLEX SPACE FORM IN TERMS OF THE STRUCTURE JACOBI OPERATOR

  • Ki, U-Hang;Kurihara, Hiroyuki
    • 대한수학회논문집
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    • 제37권1호
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    • pp.229-257
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    • 2022
  • Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form Mn+1(c), c ≠ 0. We denote by A and R𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R𝜉A = AR𝜉 and at the same time ∇𝜉R𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.