非平坦复空间形式实数超曲面上Reeb向量场的Jacobi算子

Pub Date : 2016-06-23 DOI:10.5666/KMJ.2016.56.2.541

U. Ki, Soo-Jin Kim, Hiroyuki Kurihara

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引用次数: 2

摘要

设M是具有近似接触度量结构(φ， ξ， η， g)的复空间形式的实超曲面。本文证明了如果结构Jacobi算子Rξ = R(·，ξ)ξ是φ∇ξ -平行且Rξ与结构张量φ交换，则M是在TrRξ为常数的条件下的a型齐次实超曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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 Rξ = R(·, ξ)ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor φ, then M is a homogeneous real hypersurface of Type A provided that TrRξ is constant.

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