  I show that on any smooth, projective ordinary curve of genus at least two
and a projective embedding, there is a natural example of a stable Ulrich
bundle for this embedding: namely the sheaf $B^1_X$ of locally exact
differentials twisted by $\O_X(1)$ given by this embedding and in particular
there exist ordinary varieties of any dimension which carry Ulrich bundles. In
higher dimensions, assuming $X$ is Frobenius split variety I show that $B^1_X$
is an ACM bundle and if $X$ is also a Calabi-Yau variety and $p>2$ then $B^1_X$
is not a direct sum of line bundles. In particular I show that $B^1_X$ is an
ACM bundle on any ordinary Calabi-Yau variety. I also prove a characterization
of projective varieties with trivial canonical bundle such that $B^1_X$ is ACM
(for some projective embedding datum): all such varieties are Frobenius split
(with trivial canonical bundle).
