2021/04/05 by Behzad Najafi, Najafi, B., Abdelhamid Tayebi +1
Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2104.02065
openalex publication_date 2021/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove that every connected homogeneous Finsler space with non-positive flag curvature and isotropic S-curvature is Riemannian or locally Minkowskian. We extend the Szabó's rigidity theorem for Berwald surfaces and show that homogeneous isotropic Berwald metrics with non-positive flag curvature are Riemannian or locally Minkowskian. We prove that a homogeneous (α, β)-metrics has isotropic mean Berwald curvature if and only if it has vanishing mean Berwald curvature generalizing result previously only known in the case of Randers metrics. Our second main result is to show that every homogeneous (α,β)-metric with non-positive flag curvature and almost isotropic S-curvature is Riemannian or locally Minkowskian.