Projective properties of Lorentzian surfaces

TL;DR

This paper explores the projective symmetries of Lorentzian surfaces, establishing bounds on isometry groups for tori and constructing noncompact surfaces with special projective transformations.

Contribution

It proves that non-flat tori have an isometry group index at most two in their projective group and constructs noncompact surfaces with infinite order non-isometric projective transformations.

Findings

The index of the isometry group in the projective group for non-flat tori is at most two.

Existence of noncompact surfaces with non-isometric projective transformations of infinite order.

Provides new insights into the symmetry properties of Lorentzian surfaces.

Abstract

We investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite noncompact surface can be endowed with a metric having a non isometric projective transformation of infinite order.