Mathebula, Agreement2021-04-262021-04-262020Mathebula, Agreement (2020) Symmetry classifications on a curved geometry, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/31005>https://hdl.handle.net/10539/31005A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, 2020In 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 equationsOnline resource (95 pages)enSymmetry (Mathematics)GeometryThesis