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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 136, Number 3, Pages 365–379
DOI: https://doi.org/10.4213/tmf232 (Mi tmf232) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group

A. A. Magazev, I. V. Shirokov

Omsk State University
Full-text PDF (275 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf232
Abstract: We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces $M$ with invariant and central metrics. The proposed integration algorithm consists in using a special canonical transformation in the space $T^*M$ based on constructing the canonical coordinates on the orbits of the coadjoint representation and on the simplectic sheets of the Poisson algebra of invariant functions. This algorithm is applicable to integrating geodesic flows on homogeneous spaces of a wild Lie group.
Keywords: Lie group, Lie algebra, homogeneous space, geodesic flow, invariant operator, Poisson bracket.
Received: 10.11.2002
English version:
Theoretical and Mathematical Physics, 2003, Volume 136, Issue 3, Pages 1212–1224
DOI: https://doi.org/10.1023/A:1025691013809
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Language: Russian
Citation: A. A. Magazev, I. V. Shirokov, “Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group”, TMF, 136:3 (2003), 365–379; Theoret. and Math. Phys., 136:3 (2003), 1212–1224
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v136/i3/p365
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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