  The first variant of this article contained a fatal error. Therefore, we
publish second version our paper. In the present paper, we prove that the
curvature operator of the second kind of a Riemannian manifold is strictly
positive if its sectional curvature is strictly positive and the Ricci
curvature suitably pinched. In addition, we prove several vanishing theorems
for null spaces of the Lichnerowicz, Sampson, and Hodge-de Rham Laplacians and
find estimates for their lowest eigenvalues on compact (without boundary)
Riemannian manifolds with sectional pinched curvature.
