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Title: Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators
Author: Tsonev, Dragomir
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2013
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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.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Holonomy ; Pseudo-Riemannian ; Manakov operator