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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 661–674 (Mi izv1525)  

This article is cited in 5 scientific papers (total in 5 papers)

Construction of completely integrable geodesic flows on compact symmetric spaces

A. V. Brailov


Abstract: On every compact symmetric space, Riemannian metrics are constructed for which the geodesic flow is completely integrable in the sense of Liouville. Some of the metrics constructed in the case of a sphere are conformally equivalent to metrics on $n$-axial ellipsoids.
Bibliography: 22 titles.

Full text: PDF file (1478 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 19–31

Bibliographic databases:

UDC: 514.774.8
MSC: Primary 58F07; Secondary 58F17, 34C35, 53C35
Received: 13.06.1983
Revised: 15.11.1985

Citation: A. V. Brailov, “Construction of completely integrable geodesic flows on compact symmetric spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 661–674; Math. USSR-Izv., 29:1 (1987), 19–31

Citation in format AMSBIB
\Bibitem{Bra86}
\by A.~V.~Brailov
\paper Construction of completely integrable geodesic flows on compact symmetric spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 661--674
\mathnet{http://mi.mathnet.ru/izv1525}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=864170}
\zmath{https://zbmath.org/?q=an:0638.58011}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 19--31
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000957}


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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. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Math. USSR-Izv., 38:1 (1992), 69–90  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Petar Topalov, “Families of metrics geodesically equivalent to the analogs of the Poisson sphere”, J Math Phys (N Y ), 41:11 (2000), 7510  crossref  mathscinet  zmath
    3. V. S. Matveev, P. J. Topalov, “Geodesic equivalence of metrics as a particular case of integrability of geodesic flows”, Theoret. and Math. Phys., 123:2 (2000), 651–658  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. V. Bolsinov, B. Jovanović, “Integrable geodesic flows on homogeneous spaces”, Sb. Math., 192:7 (2001), 951–968  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. 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  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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