复空间形式中常平均曲率实超曲面的结构Jacobi算子

Pub Date : 2016-12-23 DOI:10.5666/KMJ.2016.56.4.1207

T. Hwang, U. Ki, Hiroyuki Kurihara

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摘要

设M为复空间中具有恒定平均曲率的实超曲面，其形式为Mn(c)， c (c) = 0。本文证明了如果结构Jacobi算子Rξ = R(·，ξ)ξ对结构向量场ξ为φ∇ξ -平行且Rξ与结构张量场φ可交换，则M是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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Structure Jacobi Operators of Real Hypersurfaces with Constant Mean Curvature in a Complex Space Form

Let M be a real hypersurface with constant mean curvature in a complex space form Mn(c), c ̸= 0. In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ with respect to the structure vector field ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor field φ, then M is a homogeneous real hypersurface of Type A.

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