Short CommunicationsNo Access
DIRAC STRUCTURES FROM LIE INTEGRABILITY
https://doi.org/10.1142/S0219887812200058Cited by:3 (Source: Crossref)
Abstract
We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we study the Bianchi–Cartan–Vranceanu metrics and their Hopf bundles.
AMSC: 53C60, 53C05, 53C15, 53C20, 53C55, 53D18
