Mathematical Sciences: Symmetry of Differential Geometry Structures

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The research entails investigating the conformal transformations of self-dual metrics and affine structures on quaternionic manifolds. The methods entail those relating to self-dual connections on vector bundles over 4-manifolds and the associated complex manifold or twistor space. The underlying concepts are extendable to higher dimensions via the quaternionic setting. This research has a number of ramifications to general relativity theory, quantum gravity and other areas of mathematical physics.