Dirac Surfaces and Threefolds

Original · EN

We describe Dirac structures on surfaces and 3-manifolds. Every Dirac structure on a surface M is described either by a regular 1-foliation or by a section of a circle bundle obtained as a fiberwise compactification of the line bundle ²TM. Every Dirac structure on a 3-manifold M is either the union of a presymplectic manifold and a foliated Poisson manifold, or the union of a Poisson manifold and a foliated presymplectic manifold.