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Title: Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators
Authors: Tsonev, Dragomir
Keywords: Holonomy
Pseudo-Riemannian
Manakov operator
Issue Date: 2013
Publisher: © Dragomir Tsonev
Abstract: 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.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
Sponsor: The Engineering and Physical Sciences Research Council (EPSRC).
URI: https://dspace.lboro.ac.uk/2134/12465
Appears in Collections:PhD Theses (Maths)

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