On the topology of manifolds with completely integrable geodesic flows
1992 ◽
Vol 12
(1)
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pp. 109-121
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AbstractWe show that if M is a compact simply connected Riemannian manifold whose geodesic flow is completely integrable with periodic integrals, then M is rationally elliptic, i.e. the rational homotopy of M is finite dimensional. We also show that rational ellipticity is shared by simply connected compact manifolds whose cotangent bundle admits a multiplicity free compact action that leaves invariant the Hamiltonian associated with some Riemannian metric. In particular it follows that if M is a Riemannian manifold whose geodesic flow is completely integrable by the Thimm method, then M is rationally elliptic. Other questions concerning the global behaviour of geodesics on homogeneous spaces are discussed.
2006 ◽
Vol 58
(2)
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pp. 282-311
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1994 ◽
Vol 13
(3)
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pp. 289-298
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2005 ◽
Vol 16
(09)
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pp. 941-955
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1994 ◽
Vol 36
(1)
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pp. 77-80
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Keyword(s):
2013 ◽
Vol 15
(03)
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pp. 1350007
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