Courant-Nijenhuis tensors and generalized geometries

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dc.creatorGrabowski, Janusz
dc.date2006-01-31
dc.date.accessioned2026-07-07T07:39:25Z
dc.date.available2026-07-07T07:39:25Z
dc.descriptionNijenhuis tensors $N$ on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form $N+N^*=aI$ for irreducible Courant algebroids, in particular for the extended tangent bundles $TM\oplus T^*M$. It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations $N^2-aN+bI=0$, so that the corresponding hierarchy is very poor. The particular case $N^2=-I$ is associated with Hitchin's generalized geometries and the cases $N^2=I$ and $N^2=0$ -- to other "generalized geometries". These concepts find a natural description in terms of supersymplectic Poisson brackets on graded supermanifolds.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0601761
dc.identifierhttp://arxiv.org/abs/math/0601761
dc.identifierMonografías de la Real Academia de Ciencias de Zaragoza 29 (2006), 101--112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121441
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject17B99, 17B62, 53C15, 53C56, 53D05, 53D17
dc.titleCourant-Nijenhuis tensors and generalized geometries
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