Definition
Let X and Y be vector fields on an N-dimensional real manifold M and let ξ and η be p-forms. Then X+ξ and Y+η are sections of the direct sum of the tangent bundle and the bundle of p-forms. The Courant bracket of X+ξ and Y+η is defined to be
where is the Lie derivative along the vector field X, d is the exterior derivative and i is the interior product.
Read more about this topic: Courant Bracket
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