Abstract
Geodesic lemma for homogenenous Finsler \((\alpha ,\beta )\) metrics is formulated in terms of the underlying Riemannian metric \(\alpha \) and the one-form \(\beta \). The existence of a particular reductive decomposition is described for easy construction of Finslerian geodesic graph, in a suitable group extension. As a consequence, it is proved that for the underlying geodesic orbit Riemannian metric \(\alpha \), all Finsler \((\alpha ,\beta )\) metrics are also geodesic orbit metrics. An alternative construction of Finslerian geodesic graph for naturally reductive underlying Riemannian metric \(\alpha \) is also described.
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Dušek, Z. Geodesic orbit Finsler \((\alpha ,\beta )\) metrics. European Journal of Mathematics 9, 9 (2023). https://doi.org/10.1007/s40879-023-00609-0
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DOI: https://doi.org/10.1007/s40879-023-00609-0
Keywords
- Homogeneous Finsler manifold
- \((\alpha , \beta )\) metric
- Homogeneous geodesic
- G.o. manifold
- Geodesic graph