局部积黎曼流形的半不变子流形
Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold
DOI: 10.12677/PM.2022.122030, PDF, HTML,    国家自然科学基金支持
作者: 边立泽, 李淑雯, 何 勇*, 田 畅：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 黎曼流形；局部积；半不变子流形；垂直分布；混合全测地；Riemannian Manifold； Locally Product； Semi-Invariant Submanifolds； Vertical Distribution； Mixed-Geodesic
摘要: 本文主要研究局部积黎曼流形的半不变子流形的相关性质。 首先，通过Weingarten 公式，给出了局部积黎曼流形的半不变子流形的垂直分布 D⊥完全可积的充要条件AFZW∈D⊥。 其次，得到了局部积黎曼流形的半不变子流形成为混合全测地半不变子流形的充分条件。
Abstract: In this paper, we study the semi-invariant submanifolds of a locally product Riemannian manifold. Firstly, for the semi-invariant submanifolds of a locally product Riemannian manifold, the necessary and sufficient conditions for its vertical distribution to be completely integrable are given by the Weingarten formula. Secondly, a sufficient condition is obtained for the semi-invariant submanifolds of a locally product Riemannian manifold to be mixed-geodesic submanifolds.
文章引用：边立泽, 李淑雯, 何勇, 田畅. 局部积黎曼流形的半不变子流形[J]. 理论数学, 2022, 12(2): 257-263. https://doi.org/10.12677/PM.2022.122030

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