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arXiv · 2303.09368

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

Teresa Arias-Marco·Zdenek Dusek
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Abstract

Invariant geodesic orbit Finsler $(\alpha,\beta)$ metrics $F$ which arise from Riemannian geodesic orbit metrics $\alpha$ on spheres are determined. The relation of Riemannian geodesic graphs with Finslerian geodesic graphs proved in a previous work is now illustrated with explicit constructions. Interesting examples 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 be extended. It is also shown that projective spaces other than ${\mathbb{R}}P^n$ do not admit invariant purely Finsler $(\alpha,\beta)$ metrics.

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Teresa Arias-Marco, Zdenek Dusek. 2023-03-16. Geodesic graphs for geodesic orbit Finsler $(\alpha,\beta)$ metrics on spheres. https://arxiv.org/abs/2303.09368

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