Landsberg curvature of twisted product Finsler metric

2023/05/09 by Lize Bian, Yong He, Bian, Lize +3
Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.05468

openalex publication_date 2023/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M1,F1) and (M2,F2) be two Finsler manifolds. The twisted product Finsler metric of F1 and F2 is a Finsler metric F = (F1²+ f²F2²)¹/2 endowed on the product manifold M1 * M2, where f is a positive smooth function on M1 * M2. In this paper, Landsberg curvature and mean Landsberg curvature of the twisted product Finsler metric are derived. Necessary and sufficient conditions for the twisted product Finsler metric to be Landsberg metric or weakly Landsberg metric are obtained. And it is proved that every twisted product Finsler metric has relatively isotropic Landsberg (resp. relatively isotropic mean Landsberg) curvature if and only if it is a Landsberg (resp. weakly Landsberg) metric.

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