 When "p"=0 the Courant bracket reduces to the Lie bracket on a [[principal bundle|principal]] [[circle bundle]] over "M" with [[Riemann curvature tensor|curvature]] given by the 2-form twist "H".The bundle of 0-forms is the trivial bundle, and a section of the direct sum of the tangent bundle and the trivial bundle defines a circle [[invariant vector field]] on this circle bundle.Concretely, a section of the sum of the tangent and trivial bundles is given by a vector field "X" and a function "f" and the Courant bracket is
which is just the Lie bracket of the vector fields
where "θ" is a coordinate on the circle fiber.