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Article Dans Une Revue Mathematische Annalen Année : 2015

Isometry-invariant geodesics and the fundamental group

Résumé

We prove that on closed Riemannian manifolds with infinite abe-lian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true if the fundamental group is infinite cyclic. We also formulate a generalization of the isometry-invariant geodesics problem, and a generalization of the celebrated Weinstein conjecture: on a closed contact manifold with a selected contact form, any strict contactomorphism that is contact-isotopic to the identity possesses an invariant Reeb orbit.
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Dates et versions

ensl-01404297 , version 1 (28-11-2016)

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Marco Mazzucchelli. Isometry-invariant geodesics and the fundamental group. Mathematische Annalen, 2015, 362, pp.265 - 280. ⟨10.1007/s00208-014-1113-8⟩. ⟨ensl-01404297⟩
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