It is known that there are no real hypersurfaces with parallel structure Jacobi operators in a nonflat complex space form. In this paper, we classify real hypersurfaces in a nonflat complex space form whose structure Jacobi operator is cyclic-parallel.2000 Mathematics subject classification: primary 53B25; secondary 53C15, 53C25.
Let M be a real hypersurface of a complex space form with almost contact metric structure ðf; x; h; gÞ. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator R x ¼ RðÁ; xÞx is x-parallel. In particular, we prove that the condition ' x R x ¼ 0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when R x fS ¼ SfR x holds on M, where S denotes the Ricci tensor of type ð1; 1Þ on M.
Abstract. Let M be a real hypersurface of a complex space form with almost contact metric structure (ϕ, ξ, η, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator R ξ = R(·, ξ)ξ is ξ-parallel. In particular, we prove that the condition ∇ ξ R ξ = 0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when R ξ ϕS = R ξ Sϕ holds on M , where S denotes the Ricci tensor of type (1,1) on M .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.