2016/11/03 by Ming Xu, Lei Zhang, Xu, Ming +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1611.00920
arxiv created 2016/11/03 · openalex publication_date 2016/11/03 · arxiv updated 2016/11/04 · openalex created_date 2016/11/11 · openalex updated_date 2026/07/28
In this paper, we explore the similarity between normal homogeneity and δ-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected δ-homogeneous Finsler space is G-δ-homo-geneous, for some suitably chosen connected quasi-compact G. So δ-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on G and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on G instead. More careful analysis shows, in the space of all Finsler metrics on G/H, the subset of all G-δ-homogeneous ones is in fact the closure for the subset of all G-normal ones, in the local C0-topology (Theorem \refmain-thm-1). Using this approximation technique, the classification work for positively curved normal homogeneous Finsler spaces can be applied to classify positively curved δ-homogeneous Finsler spaces, which provides the same classification list. As a by-product, this argument tells more about δ-homogeneous Finsler metrics satisfying the (FP) condition (a weaker version of positively curved condition).