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Commuting Structure Jacobi Operator for Semi-Invariant Submanifolds of Codimension 3 in Complex Space Forms

송현정|기우항
영남수학회 (Youngnam Mathematical Society)|2022.09|East Asian Mathematical Journal|제38권 제5호|pp. 549-581

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참고문헌

키워드

Ricci tensorscalar curvaturesemi-invariant submanifolddistinguished normalcomplex space formstructure Jacobi operatorHopf real hypersurfaces.
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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),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 vec- tor 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 M satisfies RξS = SRξ and at the same time Rξφ = φRξ, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s − 2(n − 1)c ≤ 0.

Abstract

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),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 vec- tor 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 M satisfies RξS = SRξ and at the same time Rξφ = φRξ, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s − 2(n − 1)c ≤ 0.

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관련 논문AI추천

Submanifolds of Codimension 3 in a Complex Space Form with Commuting Structure Jacobi Operator기우항, 송현정경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제1호Structure Jacobi Operator of Semi-invarinat Submanifolds in Complex Space Forms기우항, 김수진영남수학회 · East Asian Mathematical Journal2020 · 제36권 제3호Semi-invariant submanifolds of codimension 3 in a complex space form in terms of the structure Jacobi operatorHiroyuki Kurihara, U-Hang Ki대한수학회 · 대한수학회논문집2022 · 제37권 제1호SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN A COMPLEX SPACE FORM WITH ξ-PARALLEL STRUCTURE JACOBI OPERATOR기우항, 송현정영남수학회 · East Asian Mathematical Journal2024 · 제40권 제1호Structure Jacobi Operators of Semi-invarinat Submanifolds in a Complex Space Form II기우항, 김수진영남수학회 · East Asian Mathematical Journal2022 · 제38권 제1호SEMI-INVARINAT SUBMANIFOLDS OF CODIMENSION 3 SATISFYING ∇ϕ∇ξξRξ = 0 IN A COMPLEX SPACE FORM기우항영남수학회 · East Asian Mathematical Journal2021 · 제37권 제1호

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