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We present a framework for the reduction of various geometric structuresextending the classical coisotropic Poisson reduction. For this we introduceconstraint manifolds and constraint vector bundles. A constraint Serre-Swantheorem is proven, identifying constraint vector bundles with certain finitelygenerated projective modules, and a Cartan calculus for constraintdifferentiable forms and multivector fields is introduced. All of theseconstructions will be shown to be compatible with reduction. Finally, we applythis to obtain a reduction procedure for Lie (bi-)algebroids and Diracmanifolds.

Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids