Symmetry structures and conserved forms of di erential equations on curved manifolds
No Thumbnail Available
Date
2019
Authors
Gadjagboui, Bourgeois Biova Irenee
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We explore two methods in nding Noether symmetries and conservation laws of di erential
equations on Riemannian manifolds. The rst one is based on the Noether's theorem
while the second one is about the `multiplier approach'. Using the rst method, we try
to nd the variational symmetries, here, denoted X. With geodesic equations, the second
method consists of nding the Lagrangian multipliers. This yields the conserved quantities
when one acts the multipliers on the geodesic equations. It turns out that the total
number of conserved quantities is equal to the number of variational symmetries found.
The Lie algebra of in nitesimal isometries of the Riemannian manifolds studied has the
dimension not exceeding 1
2n(n + 1), where n = 4.
In the rst case studied in Chapter 2, variational symmetries and conservation laws of
a modi ed de Sitter metric are classi ed. We came up with the suggestion that where
a nite dimensional group generated by conservation laws exists, the Noether symmetry
group has at least one additional symmetry that is not given by the Killing Vectors. This
is later con rmed in the rest of all the other cases studied.
Description
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2019
Keywords
Citation
Gadjagboui, Bourgeois Biova Irénée (2016) Symmetry structures and conserved forms of differential equations on curved manifolds,University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/30458>