Symmetry classifications on a curved geometry

Abstract

In this thesis, we consider one-parameter point transformations that leave a differential equation invariant. In particular, we show that Noether symmetry classifications of any diagonal metric may be simplified by geometric criteria. We describe the Klein-Gordon equation for some general spaces and deal with the corresponding Killing algebra. Moreover, our investigation consists of several metrics, their Lie algebras, the point generators of the Klein-Gordon equation and their associated potential functions. Finally, we study a class of ecological diffusive equations and determine higher-order symmetries of non-linear diffusion equations