23 may 2023 -- 16:15
Geometry in Como (+ online)
Abstract.
Generalized Geometry was introduced at the beginning of XXI century by N. Hitchin, M. Gualtieri and G. Cavalcanti. This theory is based on the study of the generalized tangent bundle or big tangent bundle, defined as the Whitney sum of the tangent and the cotangent bundle of a manifold.
As in the case of geometric structures defined on a manifold, different "generalized geometric structures" can be defined on the generalized tangent bundle, such as metrics, complex structures, paracomplex structures, etc. The first important examples of generalized complex structures were given by M. Gualtieri, showing that both complex structures and symplectic structures defined on a manifold can be understood as generalized complex structures. In this seminar, we shall show that many other structures appear in Generalized Geometry if we take a less restrictive definition than the original one given by M. Gualtieri. In this way, we shall compare which are the similarities and differences between working on the tangent bundle or the generalized tangent bundle of a manifold.