Bulletin of the belgian mathematical society-simon stevin vol:12 issue:4 pages:543-555
We show that on any locally conformal Kahler (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 mid anti-Lee vector fields is also harmonic and minimal when seen as a map from (M, g) with values in the Grassmanniam G(2)(or)(M) endowed with the Sasaki metric. As a particular case of l.c.K. manifolds, we look at locally conformal hyperkahler manifolds mid 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 axe harmonic and minimal and the canonical distribution is critical for the energy functional, but when seen as a map with values in G(2)(or)(M) it is minimal, but not harmonic.