On the Lichnerovicz Laplacian

Abstract

In this paper, we study the geometry of the kernel of the Lichnerovicz Laplacian in the case of complete and, in particular, compact Riemannian manifolds, and also propose a lower estimate of its eigenvalues on a compact Riemannian manifold whose curvature operator is bounded from below and an upper estimate of its eigenvalues on a compact Riemannian manifold with the Ricci curvature bounded from below. We define the Lichnerovicz Laplacian on the space of smooth sections of the bundle of covariant tensors as is required by its original definition; this distinguishes our results from results obtained earlier.