Compact Liouville surfaces

DOI10.2969/jmsj/04330555zbMath0751.53015OpenAlexW2074459975WikidataQ125741151 ScholiaQ125741151MaRDI QIDQ1179724

Kazuyoshi Kiyohara

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.2969/jmsj/04330555

zbMATH Keywords

geodesic flowLiouville metricZoll's metric

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

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Metric with ergodic geodesic flow is completely determined by unparameterized geodesics ⋮ Projectively equivalent metrics on the torus ⋮ The gap phenomenon in the dimension study of finite type systems ⋮ Koenigs theorem and superintegrable Liouville metrics ⋮ Cut loci and conjugate loci on Liouville surfaces ⋮ On the number of nontrivial projective transformations of closed manifolds ⋮ Invariant characterization of Liouville metrics and polynomial integrals ⋮ Special Liouville metric with the Ricci condition ⋮ Two-dimensional superintegrable metrics with one linear and one cubic integral ⋮ Differential invariants for cubic integrals of geodesic flows on surfaces ⋮ Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and applications ⋮ Singular semi-classical approximation on Liouville surfaces ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces

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