Contact metric manifolds whose characteristic vector field is a harmonic vector field

In this paper, contact metric manifolds whose characteristic vector field (zeta) is a harmonic vector field are called H-contact manifolds. We show that a (2n+1)-dimensional contact metric manifold is an H-contact manifold if and only if (zeta) is an eigenvector of the Ricci operator (J.C. Gonzalez-Davila and L. Vanhecke [J. Geom. 72 (2001) 65–76] proved this result for n=1). Consequently, the class of H-contact manifolds is very large. Moreover, we give some application about the topology of a compact H-contact manifold.