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

2010/01/31 by Vladimir S. Matveev, Matveev, Vladimir S. · 1 citation
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.1002.0133

This paper has been withdrawn by the author. this paper, together with the paper arXiv:0911.3521, is now a part of the paper arXiv:1002.3934

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

Abstract

I prove the two-dimensional pseudo-Riemannian version of the projective Obata conjecture stating that on a closed manifold different from the round sphere every projective (i.e., geodesic-preserving) vector field is Killing.

Citations

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

Cited by

• Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial 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

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