Eigenvalues of the Laplacian on forms

Some bounds for eigenvalues of the Laplace operator acting on forms on a compact Riemannian manifold are derived.In case of manifolds without boundary we give upper bounds in terms of the curvature, its covariant derivative and the injectivity radius.For a small geodesic ball upper and lower bounds of eigenvalues in terms of bounds of sectional curvature are given.