Let (M,g) be a compact manifold of dimension n with metric tensor g. Let $Delta^p = ddelta + delta d$ be the Laplace-Beltrami operator acting on the space of smooth p-forms. Then we have the spectrum of $Delta^p$ for each $0 leq p leq n$ $$ Spec^p(M,g) = {0 let lambda_{1,p} leq lambda_{2,p} leq cdots uparrow + infty}, $$ where each eigenvalue is repeated according to its multiplicity. Many authors [3,4,5,6] have studied relationship between the spectrum of M and the geometry of M. In[3], J. S. Pak, J.-H. Kwon and K.-H. Cho studied the spectrum of the Laplacian and the curvature of a compact orientable cosymplectic manifold. In this paper, we shall prove :