# On the existence and stability of two-dimensional Lorentzian tori without conjugate points

## TL;DR

This paper introduces new examples of compact Lorentzian surfaces without conjugate points, analyzes their stability, and demonstrates that such properties are neither rare nor rigid in the Lorentzian context.

## Contribution

It provides infinitely many new examples of Lorentzian tori without conjugate points and studies their stability, revealing contrasts with Riemannian geometry.

## Key findings

- New examples of Lorentzian tori without conjugate points.
- The Clifton-Pohl torus is shown to be maximally stable.
- Absence of conjugate points is not a rigid property in Lorentzian geometry.

## 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.