Reduction of Dirac structures along isotropic subbundles

TL;DR

This paper introduces a canonical method to reduce Dirac structures along isotropic subbundles in Courant algebroids, with applications to Dirac's theory of constraints and Poisson reduction.

Contribution

It provides a new systematic approach to obtain reduced Dirac subbundles, extending the theory of Dirac structures and their applications.

Findings

A canonical reduction procedure for Dirac subbundles

Application to Dirac's theory of constraints

Extension to Marsden-Ratiu reduction in Poisson geometry

Abstract

Given a Dirac subbundle and an isotropic subbundle of a Courant algebroid, we provide a canonical method to obtain a new Dirac subbundle. When the original Dirac subbundle is involutive (i.e., a Dirac structure) this construction has interesting applications, for instance to Dirac's theory of constraints and to the Marsden-Ratiu reduction in Poisson geometry.