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, 下载: 312  浏览: 507  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

参考文献

[1] Nijenhuis, A. (1951) Xn−1-Forming Sets of Eigenvectors. Indagationes Mathematicae, 54, 200- 212.
https://doi.org/10.1016/S1385-7258(51)50028-8
[2] Yano, K. (1958) On Walker Differentiation in Almost Product or Almost Complex Spaces. Indagationes Mathematicae, 61, 573-580.
https://doi.org/10.1016/S1385-7258(58)50082-1
[3] Yano, K. (1959) Affine Connexions in an Almost Product Space. Kodai Mathematical Journal, 11, 1-24.
https://doi.org/10.2996/kmj/1138844134
[4] Hsu, C. (1964) Remarks on Certain Almost Product Spaces. Pacific Journal of Mathematics, 14, 163-176.
https://doi.org/10.2140/pjm.1964.14.163
[5] Tachibana, S. (1960) Some Theorems on Locally Riemannian Spaces. Tohoku Mathematical Journal, 12, 281-292.
https://doi.org/10.2748/tmj/1178244441
[6] Adati, T. (1981) Submanifolds of an Almost Product Riemannian Manifold. Kodai Mathematical Journal, 4, 327-343.
https://doi.org/10.2996/kmj/1138036379
[7] Bejancu, A. (1984) Semi-Invariant Submanifolds of Locally Product Riemannian Manifold. An Univ Timisoara Ser Stiint Math Al, 22, 3-11.
[8] Matsumoto, K. (1982) On Submanifolds of Locally Product Riemannian Manifolds. TRU Mathematics, 18, 145-157.
[9] Sahin, B. and Atceken, M. (2003) Semi-Invariant Submanifolds of Riemannian Product Manifold. Balkan Journal of Geometry and Its Applications, 24, 549-558.
[10] Atceken, M. (2005) Submanifolds of Riemannian Product Manifolds. Turkish Journal of Mathematics, 29, 389-401.
[11] Atceken, M. (2010) Geometry of Semi-Invariant Submanifolds of a Riemannian Product Manifold. Mathematica Moravica, 14, 23-34.
https://doi.org/10.5937/MatMor1001023A
[12] Atceken, M. (2008) A Condition for Warped Product Semi-Invariant Submanifolds to Be Riemannian Product Semi-Invariant Submanifolds in Locally Riemannian Product Manifolds. Turkish Journal of Mathematics, 32, 349-362.
[13] Tastan, H.M. and Gerdan, S. (2018) Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. Mathematical Advances in Pure and Applied Sciences, 1, 23-26.
[14] Traore, M., Tastan, H.M. and Gerdan, S. (2021) Multiply Warped Product Generalized Semi-Invariant Submanifolds. International Electronic Journal of Geometry, 14, 313-330.
[15] 臼正国, 沈一冰. 黎曼几何初步[M]. 北京: 高等教育出版社, 2004.
[16] 陈维桓. 微分流形初步[M]. 北京: 高等教育出版社, 2001.

为你推荐