Dirac structures and generalized complex structures on
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Izu Vaisman
Abstract
We consider Courant and Courant–Jacobi brackets on the stable tangent bundle TM × ℝh of a differentiable manifold and corresponding Dirac, Dirac–Jacobi and generalized complex structures. We prove that Dirac and Dirac–Jacobi structures on TM × ℝh can be prolonged to TM × ℝk, k > h, by means of commuting infinitesimal automorphisms. Some of the stable generalized complex structures are a natural generalization of the normal almost contact structures; they are expressible by a system of tensors (P, θ, F, Za, ξa) (a = 1, …, h), where P is a Poisson bivector field, θ is a 2-form, F is a (1, 1)-tensor field, Za are vector fields and ξa are 1-forms, which satisfy conditions that generalize the conditions satisfied by a normal almost contact structure (F, Z, ξ). We prove that such a generalized structure projects to a generalized complex structure of a space of leaves and we characterize the structure by means of the projected structure and of a normal bundle of the foliation. Like in the Boothby–Wang theorem about contact manifolds, principal torus bundles with a connection over a generalized complex manifold provide examples of this kind of generalized normal almost contact structures.
© Walter de Gruyter
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Dirac structures and generalized complex structures on
Artikel in diesem Heft
- Painlevé equations and the middle convolution
- Manifolds with asymptotically nonnegative minimal radial curvature
- Hermitian indicator sets
- A question of Kantor on elations of dual translation generalized quadrangles
- Equi-isoclinic planes in Euclidean even dimensional spaces
- Antipodal trees and mutually critical points on surfaces
- Intersection properties of polyhedral norms
- Special curves defined over a finite field: plane models and gonality
-
On a new class of embedded hypersurfaces in
with nonzero constant mean curvature - On a 25-dimensional embedding of the Ree–Tits generalized octagon
-
Dirac structures and generalized complex structures on
