  An important operation in generalized complex geometry is the Courant bracket
which extends the Lie bracket that acts only on vectors to a pair given by a
vector and a p-form. We explore the possibility of promoting the elements of
the Courant bracket to physical fields by constructing a geometric action based
on the Kirillov-Kostant symplectic form. For the $p=0$ forms, the action
generalizes Polyakov's two-dimensional quantum gravity when viewed as the
geometric action for the Virasoro algebra. We show that the geometric action
arising from the centrally extended Courant bracket for the vector and zero
form pair is similar to the geometric action obtained from the semi-direct
product of the Virasoro algebra with a U(1) affine Kac-Moody algebra. For
arbitrary $p$ restricted to a Dirac structure, we derived the geometric action
and exhibit generalizations for almost complex structures built on the
Kirillov-Kostant symplectic form. In the case of p+1 dimensional submanifolds,
we also discuss a generalization of a Kahler structure on the orbits.
