On completeness and dynamics of compact Brinkmann spacetimes

TL;DR

This paper proves geodesic completeness for compact Brinkmann Lorentz manifolds and explores the dynamical properties of their parallel vector fields, contributing to the understanding of their geometric and dynamical structure.

Contribution

It establishes geodesic completeness for compact and compactly homogeneous Brinkmann spaces and analyzes the flow generated by their parallel vector fields.

Findings

Geodesic completeness of compact Brinkmann spaces

Parallel vector fields generate equicontinuous flows

Partial results on the dynamics of the parallel vector field

Abstract

Brinkmann Lorentz manifolds are those admitting an isotropic parallel vector field. We prove geodesic completeness of the compact and also compactly homogeneous Brinkmann spaces. We also prove, partially, that their parallel vector field generates an equicontinuous flow.