Geodesic
Non-polynomial integrals of multidimensional geodesic flows and Lie algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1088-1093

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In this paper, we construct explicit local examples of multidimensional Riemannian metrics whose geodesic flows have non-polynomial first integrals and are completely integrable. We rely on a construction described in a recent paper by A.V. Galajinsky which allows one to construct such examples via the Casimir invariants of finite-dimensional Lie algebras.
Keywords: Riemannian metric, geodesic flow, non-polynomial first integral, Lie algebra
Mots-clés : Casimir invariant. 
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     author = {S. V. Agapov},
     title = {Non-polynomial integrals of multidimensional geodesic flows and {Lie} algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1088--1093},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a25/}
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S. V. Agapov. Non-polynomial integrals of multidimensional geodesic flows and Lie algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1088-1093. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a25/