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.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
The Engineering and Physical Sciences Research Council (EPSRC).