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http://dx.doi.org/10.7858/eamj.2022.005

STRUCTURE JACOBI OPERATORS OF SEMI-INVARINAT SUBMANIFOLDS IN A COMPLEX SPACE FORM II  

Ki, U-Hang (The National Academy of Sciences)
Kim, Soo Jin (Department of Mathematics Chosun University Gwangju)
Publication Information
East Asian mathematical journal / v.38, no.1, 2022 , pp. 43-63 More about this Journal
Abstract
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). We denote by Rξ the structure Jacobi operator with respect to the structure vector field ξ and by ${\bar{r}}$ the scalar curvature of M. Suppose that Rξ is φ∇ξξ-parallel and at the same time 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 Rξφ = φRξ, then M is a Hopf hypersurface of type (A) in Mn+1(c) provided that ${\bar{r}-2(n-1)c}$ ≤ 0.
Keywords
Semi-invariant submanifold; almost contact metric structure; structure Jacobi operator; Hopf hypersurface; scalar curvature;
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