  Here, a Finsler manifold (M, F) is considered with corresponding curvature
tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain
subspaces of the tangent spaces of M determined by the curvature are introduced
and called k-nullity foliations of the curvature operator. It is shown that if
the dimension of foliation is constant then the distribution is involutive and
each maximal integral manifold is totally geodesic. Characterization of the
k-nullity foliation is given, as well as some results concerning constancy of
the flag curvature, and completeness of their integral manifolds, providing
completeness of (M, F). The introduced k-nullity space is a natural extension
of nullity space in Riemannian geometry, introduced by S. S. Chern and N. H.
Kuiper and enlarged to Finsler setting by H. Akbar-Zadeh and contains it as a
special case.
