English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we explore the similarity between normal homogeneity and$\delta$-homogeneity in Finsler geometry. They are both non-negatively curvedFinsler spaces. We show that any connected $\delta$-homogeneous Finsler spaceis $G$-$\delta$-homo-geneous, for some suitably chosen connected quasi-compact$G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariantsingular metric on $G$ and submersion, just as normal homogeneous metrics,using a bi-invariant Finsler metric on $G$ instead. More careful analysisshows, in the space of all Finsler metrics on $G/H$, the subset of all$G$-$\delta$-homogeneous ones is in fact the closure for the subset of all$G$-normal ones, in the local $C^0$-topology (Theorem \ref{main-thm-1}). Usingthis approximation technique, the classification work for positively curvednormal homogeneous Finsler spaces can be applied to classify positively curved$\delta$-homogeneous Finsler spaces, which provides the same classificationlist. As a by-product, this argument tells more about $\delta$-homogeneousFinsler metrics satisfying the (FP) condition (a weaker version of positivelycurved condition).

$\delta$-homogeneity in Finsler geometry and the positive curvature problem