Some geometric structures of wave equations on manifolds of `neutral signatures'

TL;DR

This paper explores the geometric properties and symmetries of wave equations on manifolds with neutral signature metrics, extending the analysis beyond the well-studied Lorentzian case.

Contribution

It provides the first detailed geometric analysis of wave equations on manifolds with neutral signatures, focusing on symmetries and geometric structures.

Findings

Identification of symmetry groups for wave equations on neutral signature manifolds

Characterization of geometric structures associated with these wave equations

Extension of known Lorentzian results to neutral signature contexts

Abstract

In this paper, we study the symmetries and perform other geometric analyses of the wave equation on some spacetimes {with non diagonal metric $g_{ij}$ which are of neutral signatures}. Wave equations on the standard Lorentzian manifolds have been done but not on the manifolds from metrics of neutral signatures.