The spaces of non-contractible closed curves in compact space forms

DOI10.1070/SM8708zbMath1381.53072arXiv1604.05237MaRDI QIDQ2957865

Iskander A. Taimanov

Publication date: 30 January 2017

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.05237

zbMATH Keywords

closed geodesicsrational cohomologiesspaces of closed curves

Mathematics Subject Classification ID

Loop spaces (55P35) Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (9)

The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form ⋮ Resonance identity and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form \(S^{2n+1}/ \Gamma \) ⋮ Index iteration theories for periodic orbits: old and new ⋮ The growth of the number of periodic orbits for annulus homeomorphisms and non-contractible closed geodesics on Riemannian or Finsler \(\mathbb{R} P^2\) ⋮ The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ The non-contractibility of closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ A review of the index method in closed geodesic problem ⋮ Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Cites Work

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• The type numbers of closed geodesics
• Two closed geodesics on \(\mathbb RP^{2n+1}\) with a bumpy Finsler metric
• Geschlossene Geodätische auf Mannigfaltigkeiten mit unendlicher Fundamentalgruppe. (Closed geodesics on manifolds with infinite fundamental group)
• Real homotopy theory of Kähler manifolds
• Equivariant Morse theory and closed geodesics
• Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions
• The existence of two closed geodesics on every Finsler 2-sphere
• On the iteration of closed geodesics and the sturm intersection theory

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