Abstract:In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field $\xi $ belongs to the $(k,\mu )$-nullity distribution. Next it is shown that the dimension of the $(k,\mu )$-nullity distribution is equal to one and therefore is spanned by the characteristic vector field $\xi $.
Keywords: contact Riemannian manifold, harmonic curvature, $D$-homothetic deformation
AMS Subject Classification: 53C05, 53C20, 53C21