  We define integrable, big-isotropic structures on a manifold $M$ as
subbundles $E\subseteq TM\oplus T^*M$ that are isotropic with respect to the
natural, neutral metric (pairing) $g$ of $TM\oplus T^*M$ 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.
