Local perturbation of a Finsler metric with a closed geodesic without self-intersections

Souza, Fausto M. de

doi:10.1080/09720502.2008.10700556

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Proof Of Theorem1

Generic Conditions For Riemannian and Finsler Metrics And Th...1

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Cited by 3 publications

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“…In [28] it was already shown that one can perturb a closed geodesic of a Finsler metric to become non-degenerate using the osculating Riemannian metric. The proof of Theorem 3 could also follow the approach presented by Rifford and Ruggiero [26].…”

Section: Proof Of Theoremmentioning

confidence: 99%

The second closed geodesic, the fundamental group, and generic Finsler metrics

Rademacher

Тайманов

2022

Math. Z.

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For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a $$C^4$$ C 4 -generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.

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Section: Proof Of Theoremmentioning

confidence: 99%

The second closed geodesic, the fundamental group, and generic Finsler metrics

Rademacher

Тайманов

2022

Math. Z.

View full text Add to dashboard Cite

show abstract

“…Therefore Lemma 1 and Lemma 2 in Anosov's proof of the bumpy metrics theorem carry over to the Finsler setting which is sufficient for the proof of the Theorem. In [28] it was already shown that one can perturb a closed geodesic of a Finsler metric to become non-degenerate using the osculating Riemannian metric. The proof of Theorem 4 could also follow the approach presented by Rifford and Ruggiero [26].…”

Section: Generic Conditions For Riemannian and Finsler Metrics And Th...mentioning

confidence: 99%