Dirac Structures and Generalized Complex Structures on $TM\times\mathds{R}^h$
| dc.creator | Vaisman, Izu | |
| dc.date | 2006-07-08 | |
| dc.date.accessioned | 2026-07-07T07:18:11Z | |
| dc.date.available | 2026-07-07T07:18:11Z | |
| dc.description | We consider Courant and Courant-Jacobi brackets on the stable tangent bundle $TM\times\mathds{R}^h$ of a differentiable manifold and corresponding Dirac, Dirac-Jacobi and generalized complex structures. We prove that Dirac and Dirac-Jacobi structures on $TM\times\mathds{R}^h$ can be prolonged to $TM\times\mathds{R}^k$, $k>h$, 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 $(P,θ,F,Z_a,ξ^a)$ $(a=1,...,h)$, where $P$ is a bivector field, $θ$ is a 2-form, $F$ is a $(1,1)$-tensor field, $Z_a$ are vector fields and $ξ^a$ 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 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. | |
| dc.description | LaTex, 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607216 | |
| dc.identifier | http://arxiv.org/abs/math/0607216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114210 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53C15, 53D17 | |
| dc.title | Dirac Structures and Generalized Complex Structures on $TM\times\mathds{R}^h$ | |
| dc.type | text |