Mathematical Sciences: Twistor Theory with Applications to Restricted Holonomy Geometries and Other Problems in Differential Geometry

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The proposed research entails a study of manifolds with affine connections of restricted holonomy and the geometry of submanifolds of certain classes of Riemanian symmetric spaces. Particular attention in the latter case will be paid to surfaces in quaternionic-Kaehler manifolds where such surfaces can be studied by complex-analytic means relative to an associated complex manifold. This research also entails a study of deformations of Einstein metrics on 4-manifolds.