一类双卷积空间非退化曲面的曲率表示
Curvature Representation of Nondegenerate Surfaces in a Class of Double Warped Product Spaces
DOI: 10.12677/AAM.2022.113131, PDF,   
作者: 杜玲伟, 王 剑：天津职业技术师范大学，理学院，天津
关键词: 双卷积空间；子流形；数量曲率；Double Warped Product Space； Submanifolds； Scalar Curvature
摘要: 针对一类配置卷积度量的双卷积空间，利用Kozul计算方法和微分几何的理论研究了非退化曲面的卷积曲率形式，得到其刻画方程。在此基础上，证明了卷积函数为一次函数对应的双卷积空间平坦。
Abstract: For a class of double Warped Product spaces with a Riemannian metric, the paper gives the curvature representation of the nondegenerate surface of double Warped Product space by using the knowledge of Kozul formula and the theory of differential geometry. On this basis, it is proved that the nondegenerate surface of double Warped Product space is flat if and only if Warped function is the first order function.
文章引用：杜玲伟, 王剑. 一类双卷积空间非退化曲面的曲率表示[J]. 应用数学进展, 2022, 11(3): 1209-1213. https://doi.org/10.12677/AAM.2022.113131

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