Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators
thesisposted on 2013-06-11, 15:28 authored by Dragomir Tsonev
In the present thesis we construct a new class of holonomy algebras in pseudo-Riemannian geometry. Starting from a smooth connected manifold M, we consider its (1;1)-tensor fields acting on the tangent spaces. We then prove that there exists a class of pseudo- Riemannian metrics g on M such that the (1;1)-tensor fields are g-self adjoint and their centralisers in the Lie algebra so(g) are holonomy algebras for the Levi-Civita connection of g. Our construction is elaborated with the aid of Manakov operators and holds for any signature of the metric g.
The Engineering and Physical Sciences Research Council (EPSRC).
- Mathematical Sciences
Publisher© Dragomir Tsonev
NotesA Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
EThOS Persistent IDuk.bl.ethos.574215