On the existence and stability of two-dimensional Lorentzian tori without conjugate points
Differential Geometry
2019-02-13 v1
Abstract
Infinitely many new examples of compact Lorentzian surfaces without conjugate points are given. Further, we study the existence and the stability of this property among Lorentzian metrics with a Killing field. We obtain a new obstruction and prove that the Clifton- Pohl torus and some of our examples are as stable as possible. This shows that in constrast with the Riemannian Hopf theorem, the absence of conjugate points in the Lorentzian setting is neither "special" nor rigid.
Cite
@article{arxiv.1902.04505,
title = {On the existence and stability of two-dimensional Lorentzian tori without conjugate points},
author = {Lilia Mehidi},
journal= {arXiv preprint arXiv:1902.04505},
year = {2019}
}