Relationship between sectional curvature and null spaces of Lichnerowicz-type Laplacians and their smallest eigenvalues

Abstract

In the paper, we prove that the curvature operator of the second kind of Riemannian manifolds is positive (respectively, negative) if and only if its sectional curvature is also positive (respectively, negative). In addition, we prove several vanishing theorems on null spaces of the Lichnerowicz, Sampson and Hodge-de Rham Laplacians and we find estimates of their lowest eigenvalues on closed Riemannian manifolds of sign-definite sectional curvature