紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2018, 55(1), p. 177-194

δ-HOMOGENEITY IN FINSLER GEOMETRY AND THE POSITIVE CURVATURE PROBLEM

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2018-01

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-homogeneous, 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 1.1). 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).

10.18910/67753

67753

δ-HOMOGENEITY IN FINSLER GEOMETRY AND THE POSITIVE CURVATURE PROBLEM

Osaka University and Osaka City University, Departments of Mathematics

英語

2018-01

Osaka Journal of Mathematics

55

1

177

194

https://hdl.handle.net/11094/67753

10.18910/67753

https://doi.org/10.18910/67753