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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 2, Pages 403–409
DOI: https://doi.org/10.1070/IM1988v030n02ABEH001021 (Mi im1303) 		 
This article is cited in 28 scientific papers (total in 29 papers)

Topological obstructions to integrability of geodesic flows on non-simply-connected manifolds

I. A. Taimanov
English version PDF (460 kB) Citations (29)
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DOI: https://doi.org/10.1070/IM1988v030n02ABEH001021
Abstract: In this paper, (Liouville) integrability of geodesic flows on non-simply-connected manifolds is studied. In particular, the following result is obtained: A geodesic flow on a real-analytic Riemannian manifold cannot be integrable in terms of analytic functions if either 1) the fundamental group of the manifold contains no commutative subgroup of finite index, or 2) the first Betti number of the manifold over the field of rational numbers is greater than the dimension (the manifold is assumed to be closed).
Bibliography: 11 titles.
Received: 07.02.1985
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 2, Pages 429–435
Bibliographic databases:
UDC: 531.01
MSC: 58F17
Language: English
Original paper language: Russian
Citation: I. A. Taimanov, “Topological obstructions to integrability of geodesic flows on non-simply-connected manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 429–435; Math. USSR-Izv., 30:2 (1988), 403–409
Citation in format AMSBIB
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\pages 429--435
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    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:680
    Russian version PDF:225
    English version PDF:26
    References:88
    First page:3
     
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