Courant-Nijenhuis tensors and generalized geometries
نویسنده
چکیده
Nijenhuis tensors N on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form N + N = λI for irreducible Courant algebroids, in particular for the extended tangent bundles T M = TM ⊕ TM . It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations N −λN + γI = 0, so that the corresponding hierarchy is very poor. The particular case N = −I is associated with Hitchin’s generalized geometries and the cases N = I and N = 0 – to other ”generalized geometries”. These concepts find a natural description in terms of supersymplectic Poisson brackets on graded supermanifolds. MSC 2000: Primary 17B99; Secondary 17B62, 53C15, 53C56, 53D05, 53D17.
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Courant algebroid and Lie bialgebroid contractions
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