Degree of mobility for metrics of lorentzian signature and parallel (0,2)-tensor fields on cone manifolds

TL;DR

This paper classifies the possible degrees of mobility for Lorentzian metrics on simply connected cone manifolds, relating it to projective and isometry group dimensions, and describes parallel tensor fields in this context.

Contribution

It provides a complete classification of the degree of mobility for Lorentzian metrics on cone manifolds and describes parallel tensor fields in these settings.

Findings

Classified all possible degrees of mobility for Lorentzian metrics.

Calculated differences between projective and isometry group dimensions.

Described all parallel symmetric (0,2)-tensor fields on cone manifolds.

Abstract

Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We describe all possible values of the degree of mobility on a simply connected n-dimensional manifold of lorentz signature. As an application we calculate all possible differences between the dimension of the projective and the isometry groups. One of the main new technical results in the proof is the description of all parallel symmetric (0,2)-tensor fields on cone manifolds of signature $(n-1,2).