QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Nijenhuis and compatible tensors on Courant algebroids

Joana Nunes da Costa

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It is known that Nijenhuis tensors on Lie algebroids give rise to Nijenhuis tensors on Courant algebroids. We show that Poisson bivector fields and presymplectic forms on Lie algebroids can also be viewed as Nijenhuis tensors on Courant algebroids. This observation allows us to characterize some well known structures defined by pairs of tensors on Lie algebroids as Nijenhuis tensors Courant algebroids. We study compatibility of all these structures in terms of their associated tensors on Courant algebroids.