Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta

2009/11/18 by Vladimir S. Matveev, Matveev, Vladimir S. · 2 citations
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.0911.3521

This paper has been withdrawn by the author. This paper is now, together with the paper arXiv:1002.0133, a part of the paper arXiv:1002.3934

arxiv created 2010/10/22 · arxiv updated 2010/10/25

Abstract

We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces and prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces

Citations

• Proof of projective Obata conjecture for two-dimensional pseudo-Riemannian metrics

Cited by

• Proof of projective Obata conjecture for two-dimensional pseudo-Riemannian metrics
• 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

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