  The $\pi$-exterior derivative ${\o}d$, which is the Finslerian generalization
of the (usual) exterior derivative $d$ of Riemannian geometry, is defined. The
notion of a ${\o}d$-closed vector field is introduced and investigated. Various
characterizations of ${\o}d$-closed vector fields are established. Some results
concerning ${\o}d$-closed vector fields in relation to certain special Finsler
spaces are obtained.
