  We study two kinds of transformation groups of a compact locally conformally
Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel
Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we
introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of
diffeomorphisms preserving the specific G-structure of l.c.K. manifolds. We
show that compact l.c.K. manifolds admitting a non-compact CC^* flow of LCR
transformations are rigid: it is holomorphically conformal to a Hopf manifold
with parallel Lee form.
