Geometric and Non-Geometric Compactifications of IIB Supergravity

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Complimentary geometric and non-geometric consistent reductions of IIB supergravity are studied. The geometric reductions on the identified group manifold X are found to have a gauge symmetry with Lie algebroid structure, generalising that found in similar reductions of the Bosonic string theory and eleven-dimensional supergravity. Examples of such compactifications are considered and the symmetry breaking in each case is analysed. Complimentary to the reductions on X are the nine-dimensional S-duality twisted reductions considered in the second half of the paper. The general reduced theory is given and symmetry breaking is investigated. The non-geometric S-duality twisted reductions and their relation to geometric reductions of F-Theory on X is briefly discussed.