Defesa de Tese.

Banca de defesa: Henrique Bursztyn - ORIENTADOR- IMPA Thiago Drummond- COORIENTADOR - UFRJ Vinicius Ramos - IMPA Paula Balseiro - UFF Pedro Frejlich- UFRGS Igor Mencattini - ICMC

Abstract: We present a notion of compatibility between (1,1)-tensor fields and (almost) Dirac structures, which extends the Poisson-Nijenhuis and presymplectic-Nijenhuis structures. We study several aspects of Dirac-Nijenhuis structures, such as their relation with holomorphic Dirac structures, the geometry of their foliation and quotient, and we construct hierarchies of Dirac-Nijenhuis structures. We consider their integration to presymplectic-Nijenhuis groupoids, and this includes the special case of integration of holomorphic Dirac structures. We also introduce a notion of compatibility between Nijenhuis tensors and Courant algebroids. We connect the Courant-Nijenhuis and Dirac-Nijenhuis structures with the Lie-Nijenhuis bialgebroid structures through the Manin triples .