平衡挠积埃尔米特流形
Balanced Twisted Product Hermitian Manifold
DOI: 10.12677/PM.2023.1310297, PDF,    国家自然科学基金支持
作者: 李淑雯, 加依达尔·里扎别克：新疆师范大学数学科学学院，新疆 乌鲁木齐；卢晓英：陆军边海防学院乌鲁木齐校区，新疆 乌鲁木齐；何 勇*：1新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 埃尔米特流形；挠积；平衡流形；Hermitian Manifold； Twisted Product； Balanced Manifold
摘要: 设(M1,g) 和(M2,h) 是两个埃尔米特流形,挠积埃尔米特流形(M1×fM2,G) 是赋予了埃尔米特度量 G = g+f2h 的乘积流形M1×M2，这里f是M1×M2上的光滑函数。本文推导出挠积埃尔米特流形的挠率和挠率(1,0)形式，给出埃尔米特流形(M1×fM2,G)平衡的充分必要条件。
Abstract: Let (M1,g) and (M2,h) be two Hermitian manifolds. The twisted product Hermitian manifold (M1×fM2,G) is the product manifold M1×M2 endowed with the Hermitian metric G = g+f2h , where f is a positive smooth function on M1×M2. In this paper, the torsion tensor and torsion (1,0) forms of the twisted product Hermitian manifold are derived. Sufficient and necessary conditions are given that (M1×fM2,G) is balanced.
文章引用：李淑雯, 卢晓英, 何勇, 加依达尔·里扎别克. 平衡挠积埃尔米特流形[J]. 理论数学, 2023, 13(10): 2908-2915. https://doi.org/10.12677/PM.2023.1310297

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