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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 1088–1093
DOI: https://doi.org/10.33048/semi.2022.19.087 (Mi semr1560) 		 
Geometry and topology

Non-polynomial integrals of multidimensional geodesic flows and Lie algebras

S. V. Agapovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, 1, Pirogova str., 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.087
Abstract: 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, Casimir invariant.
Funding agency Grant number
Russian Science Foundation 21-41-00018
Received November 4, 2022, published December 29, 2022
Bibliographic databases:
Document Type: Article
UDC: 514.7
MSC: 53D25, 37J35
Language: Russian
Citation: S. V. Agapov, “Non-polynomial integrals of multidimensional geodesic flows and Lie algebras”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 1088–1093
Citation in format AMSBIB
\Bibitem{Aga22}
\by S.~V.~Agapov
\paper Non-polynomial integrals of multidimensional geodesic flows and Lie algebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 1088--1093
\mathnet{http://mi.mathnet.ru/semr1560}
\crossref{https://doi.org/10.33048/semi.2022.19.087}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4534981}
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