QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Generalized hypersymplectic structures

Paulo Antunes

(download presentation)

We define hypersymplectic structures on Courant algebroids and show that we recover, as particular cases, all the classical results and examples of hypersymplectic structures on Lie algebroids. As on Lie algebroids, we prove a 1-1 correspondence theorem between hypersymplectic structures and (pseudo-)hyperKähler structures on Courant algebroids. This framework is also very rich in already known compatible structures on Courant algebroids such as hypercomplex triples, generalized Kähler pairs and Nijenhuis pairs.