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

A smooth curve on a homogeneous manifold $G/H$ is called a Riemannianequigeo-desic if it is a homogeneous geodesic for any $G$-invariant Riemannianmetric. The homogeneous manifold $G/H$ is called Riemannian equigeodesic, iffor any $x\in G/H$ and any nonzero $y\in T_x(G/H)$, there exists a Riemannianequigeodesic $c(t)$ with $c(0)=x$ and $\dot{c}(0)=y$. These two notions can benaturally transferred to the Finsler setting, which provides the definitionsfor Finsler equigeodesic and Finsler equigeodesic space. We prove twoclassification theorems for Riemannian equigeodesic spaces and Finslerequigeodesic spaces respectively. Firstly, a homogeneous manifold $G/H$ withconnected simply connected quasi compact $G$ and connected $H$ is Riemannianequigeodesic if and only if it can be decomposed as a product of Euclideanfactors and compact strongly isotropy irreducible factors. Secondly, ahomogeneous manifold $G/H$ with a compact semi simple $G$ is Finslerequigeodesic if and only if it can be locally decomposed as a product, in whicheach factor is $Spin(7)/G_2$, $G_2/SU(3)$ or a symmetric space of compact type.These results imply that symmetric space and strongly isotropy irreduciblespace of compact type can be interpreted by equigeodesic properties. As anapplication, we classify the homogeneous manifold $G/H$ with a compact semisimple $G$, such that all $G$-invariant Finsler metrics on $G/H$ are Berwald.It suggests a new project in homogeneous Finsler geometry, to systematicallystudy the homogeneous manifold $G/H$ on which all $G$-invariant Finsler metricssatisfy certain geometric property.

Symmetric space, strongly isotropy irreducibility and equigeodesic properties