  In [SW2], we defined a generalized mean curvature vector field on any almost
Lagrangian submanifold with respect to a torsion connection on an almost
K\"ahler manifold. The short time existence of the corresponding parabolic flow
was established. In addition, it was shown that the flow preserves the
Lagrangian condition as long as the connection satisfies an Einstein condition.
In this article, we show that the canonical connection on the cotangent bundle
of any Riemannian manifold is an Einstein connection (in fact, Ricci flat). The
generalized mean curvature vector on any Lagrangian submanifold is related to
the Lagrangian angle defined by the phase of a parallel (n, 0) form, just like
the Calabi-Yau case. We also show that the corresponding Lagrangian mean
curvature flow in cotangent bundles preserves the exactness and the zero Maslov
class conditions. At the end, we prove a long time existence and convergence
result to demonstrate the stability of the zero section of the cotangent bundle
of spheres.
