  We first present the natural definitions of the horizontal differential, the
divergence (as an adjoint operator), and a $p$-harmonic form on a Finsler
manifold. Next, we prove a Hodge-type theorem for a Finsler manifold in the
sense that a horizontal $p$-form is harmonic if and only if the horizontal
Laplacian vanishes. This viewpoint provides a new appropriate natural
definition of harmonic vector fields in Finsler geometry.
  This approach leads to a Bochner-Yano type classification theorem based on
the harmonic Ricci scalar.
  Finally, we show that a closed orientable Finsler manifold with a positive
harmonic Ricci scalar has a zero Betti number.
