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

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.

arXiv commentThis paper has been withdrawn by the author.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