The Hodge–de Rham Laplacian and Tachibana operator on a compact Riemannian manifold with curvature operator of definite sign

Abstract

We give a comparative analysis of the spectral properties of the Hodge– de Rham and Tachibana operators on compact Riemannian manifolds whose curvature operator is bounded and has a definite sign. We find bounds for their spectra and estimate their multiplicities.