  We exhibit two three-parameter families of locally conformal symplectic forms
on the solvmanifold $M_{n,k}$ considered in [1], and show, using the Hodge-de
Rham theory for the Lichnerowicz cohomology that that they are not $d_{\omega}$
exact, i.e. their Lichnerowicz classes are non-trivial (Theorem 1). This has
several important geometric consequences (corollary 2, 3). This also implies
that the group of automorphisms of the corresponding locally conformal
symplectic structures behaves much like the group of symplectic diffeomorphisms
of compact symplectic manifolds. We initiate the classification of the local
conformal symplectic forms in each 3-parameter family (Theorem 2, corollary 1).
We also show that the first (and) third Lichnerowicz cohomology classes are
non-zero (Theorem 3). We observe finally that the manifolds $M_{n,k}$ carry
several interesting foliations and Poisson structures.
