Lecturer:
Course Type:
PhD Course
Academic Year:
2020-2021
Period:
January-March
Duration:
35 h
Description:
Topics to be covered:
- Symplectic and Kähler structures;
- Hermitian structures;
- Almost-complex structures and integrability;
- Obstructions to the existence of an almost-complex structure;
- Cohomology of almost-complex manifolds;
- Courant bracket and Dirac structures;
- Generalized complex structures;
- Submanifolds of generalized complex structures;
- Generalized Kähler structures.
Bibliography:
- R. Bryant, On the geometry of almost-complex manifolds. Asian J. Math. 10 (2006), 561 - 605;
- M. Gualtieri, Generalized complex geometry. arXiv:math/0401221, January 2004;
- M. Gualtieri, Generalized complex geometry. Ann. of Math. 2 (2011), 75--123;
- N. Hitchin, Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), 281 -308;
- N. Hitchin, Lectures on generalized geometry. arXiv:math.DG:1008.0973, August 2010.
Research Group:
Location:
A-136