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# Geodesic graphs for geodesic orbit Finsler $(\alpha,\beta)$ metrics on spheres

Mar 2023

Invariant geodesic orbit Finsler $(\alpha,\beta)$ metrics which arise fromRiemannian geodesic orbit metrics $\alpha$ on spheres are determined. Therelation of Riemannian geodesic graphs with Finslerian geodesic graphs provedin a previous work is now illustrated with explicit constructions. Interestingexamples are found such that $(G/H,\alpha)$ is Riemannian geodesic orbit space,but for the geodesic orbit property of $(G/H,F)$ the isometry group has to beextended. It is also shown that standard projective spaces which are Riemanniangeodesic orbit spaces do not admit invariant purely Finsler $(\alpha,\beta)$metrics.

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