Group Invariant Solutions in Mathematical Physics and Differential Geometry

TL;DR

This paper reviews the theory of group invariant solutions to differential equations, emphasizing non-transverse symmetry group actions relevant in differential geometry and relativistic field theory.

Contribution

It introduces a framework accommodating non-transverse symmetry group actions, expanding the applicability of invariant solutions in physics and geometry.

Findings

Extended the theory to non-transverse group actions

Applied the framework to problems in differential geometry

Provided insights into relativistic field equations

Abstract

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key feature in our theory is that we allow for non-transverse symmetry group actions, which are very common in applications.