| Inspired by the relation between Poisson-Nijenhuis structures and holomorphic Poisson structures, I will define Dirac-Nijenhuis manifolds and Courant-Nijenhuis algebroids in such a way that they are the underlying real part of holomorphic Dirac structures and holomorphic Courant algebroids, respectively. The main tool used to introduce these new definitions is the theory of generalized derivation of degree 1 on a vector bundle. I will also explore Kahler manifolds and their relation with Courant algebroids. |
