On the Holonomy of Kaluza-Klein metrics

TL;DR

This paper explores the geometric properties of Kaluza-Klein metrics featuring a recurrent light-like vector field, enhancing understanding of their holonomy and structure in pseudo-Riemannian geometry.

Contribution

It provides new insights into the holonomy of Kaluza-Klein metrics with recurrent light-like vectors, a less-studied aspect in pseudo-Riemannian geometry.

Findings

Characterization of holonomy groups for these metrics

Conditions for recurrence of light-like vectors

Implications for geometric structures in higher dimensions

Abstract

We investigate Kaluza-Klein metrics with a recurrent light-like vector field over a pseudo-Riemannian manifold.