两类Ricci二次闵可夫斯基积芬斯勒流形
Two Classes of Ricci Quadratic Minkowskian Product FinslerManifolds
DOI: 10.12677/PM.2026.162049, PDF,    国家自然科学基金支持
作者: 郑逢雨, 何 勇*, 陈静雅, 徐延雪：新疆师范大学数学科学学院,新疆乌鲁木齐
关键词: 芬斯勒流形；闵可夫斯基积；Ricci二次；强 Ricci二次；Finsler Manifold； Minkowskian Product； Ricci Quadratic Form； Strongly Ricci Quadratic Form
摘要: 设(M1,F1)和(M2,F2)是两个芬斯勒流形,闵可夫斯基积芬斯勒流形(M,F)是赋予了芬斯勒度量F=√f(S,T)的乘积流形M= M1× M2,其中S= F12,T=F22,f是积函数.本文主要研究闵可夫斯基积芬斯勒流形的 Ricci 二次曲率,证明了闵可夫斯基积芬斯勒流形(M,F)是 Ricci二次流形当且仅当(M1,F1)和(M2,F2)都是 Ricci 二次流形;闵可夫斯基积芬斯勒流形(M,F)是强Ricci二次流形当且仅当(M1,F1)和(M2,F2)都是强 Ricci二次流形。
Abstract: Let (M1,F1) and (M2,F2) be two Finsler manifolds. The Minkowskian product Finsler manifold (M,F) is the product manifold M= M1× M2 endowed with the Finsler metric F=√f(S,T), where S= F12,T=F22, and f denotes a product function. This paper mainly investigates the Ricci quadratic curvature of Minkowskian product Finsler manifolds, and proves the following results: The Minkowskian product Finsler man- ifold (M,F) is a Ricci quadratic manifold if and only if both (M1,F1) and (M2,F2) are Ricci quadratic manifolds; The Minkowskian product Finsler manifold (M,F) is a strongly Ricci quadratic manifold if and only if both (M1,F1) and (M2,F2) are strongly Ricci quadratic manifolds.
文章引用：郑逢雨, 何勇, 陈静雅, 徐延雪. 两类Ricci二次闵可夫斯基积芬斯勒流形[J]. 理论数学, 2026, 16(2): 200-207. https://doi.org/10.12677/PM.2026.162049

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