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TMF, 2003, Volume 136, Number 3, Pages 365–379 (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

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

DOI: https://doi.org/10.4213/tmf232

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English version:
Theoretical and Mathematical Physics, 2003, 136:3, 1212–1224

Bibliographic databases:

Received: 10.11.2002

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49  mathnet  mathscinet  elib
    2. A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, “Integrable magnetic geodesic flows on Lie groups”, Theoret. and Math. Phys., 156:2 (2008), 1127–1141  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. O. L. Kurnyavko, I. V. Shirokov, “Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields”, Theoret. and Math. Phys., 156:2 (2008), 1169–1179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Jovanovic B., “Integrability of invariant geodesic flows on n-symmetric spaces”, Ann Global Anal Geom, 38:3 (2010), 305–316  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Magazev A.A., “Magnetic Geodesic Flows on Homogeneous Manifolds”, Russ. Phys. J., 57:3 (2014), 312–320  crossref  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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