Generalized Complex Geometry

Generalized complex geometry, as developed by Hitchin, contains and symplectic geometry its extremal special cases. In this thesis, we explore novel phenomena exhibited such the natural action of a B-field. We provide new examples, including some on manifolds admitting no known or structure. prove generalized Darboux theorem which yields local normal form for geometry. show that there is an elliptic deformation theory establish existence Kuranishi moduli space. We then define concept Kahler manifold. equivalent to bi-Hermitian with torsion first discovered physicists. use result solve outstanding problem in 4-dimensional geometry: exists Riemannian metric projective plane admits exactly two distinct Hermitian structures equal orientation. Finally, introduce submanifold, sub-objects correspond D-branes topological A- B-models string theory.