共形双扭曲积芬斯勒度量的局部对偶平坦性OA
Locally Dually Flatness Metrics of Conformally Doubly Warped Product Finsler Metrics
设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F=eσ√f22 F21+f21 F22,其中f1、f2和σ分别是M1、M2和M上的正值光滑函数.文章给出了共形双扭曲积芬斯勒度量F局部对偶平坦当且仅当F1和F2均局部对偶平坦且F为乘积芬斯勒度量.
Let F1 and F2 be Finsler metrics on smooth manifolds M1 and M2 respectively,the conformally doubly warped product Finsler metric is a Finsler metric F=eσ√f22 F21+f21 F22 defined on the product manifold M=M1×M2,where f1,f2 and σ are positive smooth functions on M1,M2 and M respectively.In this paper,it is proved that the conformally doubly warped product Finsler metric F is locally dually flat if and only if both F1 and F2 are locally dually flat and F is a product Finsler metric.
杨蕊嘉;何勇
新疆师范大学 数学科学学院,新疆 乌鲁木齐 830017新疆师范大学 数学科学学院,新疆 乌鲁木齐 830017
数理科学
芬斯勒度量共形双扭曲积局部对偶平坦乘积芬斯勒度量
Finsler metricConformally doubly warped productLocally dually flatProduct Finsler metric
《新疆师范大学学报（自然科学版）》 2026 (1)
91-95,112,6
新疆维吾尔自治区自然科学基金项目(2024D01A88)国家自然科学基金项目(122610881176109).
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