Isometry-invariant geodesics and the fundamental group
نویسنده
چکیده
We prove that on closed Riemannian manifolds with infinite abelian, 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.
منابع مشابه
Isometry - invariant geodesics with Lipschitz obstacle 1
Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.
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