扭积芬斯勒流形的某些曲率性质  

Curvature Properties on Finsler Warped Product Manifolds

作　　者：冯娅璐 张晓玲[1] FENG Yalu;ZHANG Xiaoling(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第1期43-48,共6页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“Finsler流形上旗曲率和共形变换的研究”(11961061);“黎曼-芬斯勒几何中若干问题的研究”(11461064).

摘　　要：基于共形平坦定义和已知结论,利用偏微分方程理论完全刻画了扭积芬斯勒度量分别是Berwald度量或局部闵可夫斯基度量的等价条件,并构造了两类非黎曼且共形于局部闵可夫斯基扭积芬斯勒度量的新的芬斯勒度量的例子.Based on the definition of conformal flatness and known conclusions,we completely characterize two equivalent conditions that Finsler warped product metrics are Berwald metrics or locally Minkowskian metrics by using theories of PDEs.Furthermore,we construct examples of two new Finsler metrics that are non-Riemannian and conformal to the locally Minkowskian Finsler warped product metrics.

关 键 词：扭积芬斯勒度量 Berwald度量 局部闵可夫斯基度量 共形平坦 

分 类 号：O186.14[理学—数学]