Isotropic subbundles of $TM\oplus T^{\ast }M$

Abstract

We define integrable, big-isotropic structures on a manifold $M$ as subbundles $E\subseteq TM\oplus T^{\ast }M$ that are isotropic with respect to the natural, neutral metric (pairing) $g$ of $TM\oplus T^{\ast }M$ and are closed by Courant brackets (this also implies that $[E,E^{{\perp }_g}]\subseteq E^{{\perp }_g}$). We give the interpretation of such a structure by objects of $M$, we discuss the local geometry of the structure and we give a reduction theorem.

LaTex, 37 pages, minimization of the defining conditions

Cited by in corpus (3)

• Weak-Hamiltonian dynamical systems
• Geometric quantization of weak-Hamiltonian functions
• The Hamiltonian formalism of the Inverse Problem