A first integral for 𝐶^{∞}, k-basic Finsler surfaces and applications to rigidity

DOI10.1090/proc/13079zbMath1366.37086OpenAlexW2317890792MaRDI QIDQ2814405

Patrick Foulon, Rafael Oswaldo Ruggiero

Publication date: 22 June 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13079

zbMATH Keywords

conjugate pointFinsler manifoldFinsler surface

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Rigidity results (53C24) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Geodesic flows in symplectic geometry and contact geometry (53D25) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (8)

Invariant volume forms and first integrals for geodesically equivalent Finsler metrics ⋮ On Finsler surfaces with certain flag curvatures ⋮ Moving planes, Jacobi curves and the dynamical approach to Finsler geometry ⋮ Reversibility at infinity and rigidity of Finsler manifolds without conjugate points ⋮ Hopf conjecture holds for analytic, \(k\)-basic Finsler tori without conjugate points ⋮ A class of Finsler metrics admitting first integrals ⋮ Gromov-hyperbolicity and transitivity of geodesic flows in \(n\)-dimensional Finsler manifolds ⋮ First integrals for Finsler metrics with vanishing \(\chi\)-curvature

Cites Work

• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Lagrangian graphs, minimizing measures and Mañé's critical values
• Convex Hamiltonians without conjugate points
• On Finsler surfaces without conjugate points
• Weak integrability of Hamiltonians on the two torus and rigidity
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