S. E. Stepanov, J. Mikeš, “The Hodge–de Rham Laplacian and Tachibana operator on a compact Riemannian manifold with curvature operator of definite sign”, Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 2,Pages <nobr>167

This article is cited in 7 papers

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

S. E. Stepanov^a, J. Mikeš^b

^a Financial University under the Government of the Russian Federation, Moscow
^b Palacký University Olomouc

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.

Keywords: Riemannian manifold, curvature operator, elliptic operators, eigenvalues and eigenforms, conformal Killing forms, harmonic forms.

UDC: 514.764.25+515.168.5

MSC: 53C20, 58A10, 58J60, 35P15

Received: 05.08.2013
Revised: 14.02.2014

DOI: 10.4213/im8156