We show that on any
locally conformal Kähler (l.c.K.) manifold $(M,J,g)$ with parallel Lee form the unit
anti-Lee vector
field is harmonic and minimal and determines a harmonic map into the unit
tangent bundle. Moreover, the canonical distribution locally
generated by the Lee and anti-Lee vector fields is also
harmonic and minimal when seen as a map from $(M,g)$ with values in
the Grassmannian $G^{or}_2(M)$ endowed with the Sasaki metric. As a
particular case of l.c.K. manifolds, we look at locally conformal
hyperkähler manifolds and show that, if the Lee form is parallel
(that is always the case if the manifold is compact), the naturally associated
three- and
four-dimensional
distributions are harmonic and minimal when regarded as maps with values
in appropriate Grassmannians. As for l.c.K. manifolds without parallel
Lee form, we consider the Tricerri metric on an Inoue surface and
prove that the unit Lee and anti-Lee vector fields are harmonic and
minimal and the canonical distribution is critical for the energy
functional, but when seen as a map with values in $G^{or}_2(M)$ it is
minimal, but not harmonic.