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Mat. Sb., 2001, Volume 192, Number 7, Pages 21–40 (Mi msb577)  

This article is cited in 19 scientific papers (total in 19 papers)

Integrable geodesic flows on homogeneous spaces

A. V. Bolsinova, B. Jovanović

a M. V. Lomonosov Moscow State University

Abstract: It is proved that the geodesic flow of a bi-invariant metric on an arbitrary homogeneous space of a compact Lie group is Liouville-integrable in the non-commutative sense.


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English version:
Sbornik: Mathematics, 2001, 192:7, 951–968

Bibliographic databases:

UDC: 513.944
MSC: Primary 37J35, 53D25; Secondary 53C30
Received: 10.05.2000

Citation: A. V. Bolsinov, B. Jovanović, “Integrable geodesic flows on homogeneous spaces”, Mat. Sb., 192:7 (2001), 21–40; Sb. Math., 192:7 (2001), 951–968

Citation in format AMSBIB
\by A.~V.~Bolsinov, B.~Jovanovi{\'c}
\paper Integrable geodesic flows on homogeneous spaces
\jour Mat. Sb.
\yr 2001
\vol 192
\issue 7
\pages 21--40
\jour Sb. Math.
\yr 2001
\vol 192
\issue 7
\pages 951--968

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    This publication is cited in the following articles:
    1. Jovanović B., “On the integrability of geodesic flows of submersion metrics”, Lett. Math. Phys., 61:1 (2002), 29–39  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. Bolsinov A.V., Jovanović B., “Noncommutative integrability, moment map and geodesic flows”, Ann. Global Anal. Geom., 23:4 (2003), 305–322  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Butler L.T., “Toda lattices and positive-entropy integrable systems”, Invent. Math., 158:3 (2004), 515–549  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    4. Mykytyuk I.V., Panasyuk A., “Bi-Poisson structures and integrability of geodesic flow on homogeneous spaces”, Transform. Groups, 9:3 (2004), 289–308  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. Bolsinov A.V., Jovanović B., “Complete involutive algebras of functions on cotangent bundles of homogeneous spaces”, Math. Z., 246:1-2 (2004), 213–236  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Bolsinov A.V., “Integrable geodesic flows on Riemannian manifolds: Construction and obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 57–103  crossref  mathscinet  zmath  isi
    7. D. I. Efimov, “The magnetic geodesic flow on a homogeneous symplectic manifold”, Siberian Math. J., 46:1 (2005), 83–93  mathnet  crossref  mathscinet  zmath  isi
    8. Butler L.T., “Invariant fibrations of geodesic flows”, Topology, 44:4 (2005), 769–789  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. Butler L.T., “Manifolds of infinite topological type with integrable geodesic flows”, Manuscripta Math., 116:1 (2005), 99–113  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. 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
    11. Bolsinov A.V., Jovanović B., “Magnetic flows on homogeneous spaces”, Comment. Math. Helv., 83:3 (2008), 679–700  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    12. Dragović V., Gajić B., Jovanović B., “Singular Manakov flows and geodesic flows on homogeneous spaces of $\mathrm{SO}(N)$”, Transform. Groups, 14:3 (2009), 513–530  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    13. Butler L.T., “Positive-entropy integrable systems and the Toda lattice, II”, Mathematical Proceedings of the Cambridge Philosophical Society, 149:3 (2010), 491–538  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    14. Jovanovic B., “Integrability of invariant geodesic flows on n-symmetric spaces”, Annals of Global Analysis and Geometry, 38:3 (2010), 305–316  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    15. Jovanovic B., “Geodesic Flows on Riemannian g.o. Spaces”, Regular & Chaotic Dynamics, 16:5 (2011), 504–513  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    16. Yuri N Fedorov, Božidar Jovanović, “Three natural mechanical systems on Stiefel varieties”, J. Phys. A: Math. Theor, 45:16 (2012), 165204  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    17. Fedorov Yu.N., Jovanovic B., “Geodesic Flows and Neumann Systems on Stiefel Varieties: Geometry and Integrability”, Math. Z., 270:3-4 (2012), 659–698  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    18. B. Gajić, V. Dragović, B. Jovanović, “On the completeness of the Manakov integrals”, J. Math. Sci., 223:6 (2017), 675–685  mathnet  crossref  mathscinet  elib
    19. Mykytyuk I.V., “Integrability of Geodesic Flows For Metrics on Suborbits of the Adjoint Orbits of Compact Groups”, Transform. Groups, 21:2 (2016), 531–553  crossref  mathscinet  zmath  isi  scopus
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