Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonat Complex Space Form

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doi:10.5666/KMJ.2016.56.2.541

Article

Kyungpook Mathematical Journal 2016; 56(2): 541-575

Published online June 1, 2016 https://doi.org/10.5666/KMJ.2016.56.2.541

Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonat Complex Space Form

U-Hang Ki¹, Soo Jin Kim², Hiroyuki Kurihara³

The National Academy of Siences, Seoul 06579, Korea¹
Department of Mathematics Chosun University, Gwangju 61452, Korea²
The College of Education, Ibaraki University, Mito 310-8512, Japan³

Received: August 18, 2015; Accepted: January 19, 2016

Abstract

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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 prove that if the structure Jacobi operator R_ξ = R(·, ξ)ξ is φ∇_ξξ-parallel and R_ξ commute with the structure tensor φ, then M is a homogeneous real hypersurface of Type A provided that TrR_ξ is constant.

Keywords: complex space form, real hypersurface, structure Jacobi operator, structure tensor, Ricci tensor.