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contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation
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 $.
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