Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form

2007/09/04 by U-Hang Ki, Ki, U-Hang, Hiroyuki Kurihara +3
Mathematics · #53B20 #53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0709.0436

openalex publication_date 2007/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=S ϕR_ξ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

Related

• Real Hypersurfaces of Non-Flat Complex Space Forms in Terms of the\n Jacobi Structure Operator
• On real hypersurfaces in non-flat complex space forms with a condition on the structure Jacobi operator OPERATOR
• Real Hypersurfaces of Non - Flat Complex Planes in Terms of the Jacobi Operators
• Conditions of parallelism of *-Ricci tensor of three dimensional real hypersurfaces in non-flat complex space forms
• Real hypersurfaces in the complex quadric with Reeb parallel structure\n Jacobi operator