Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 57 1 2015 ON ∅-RECURRENT CONTACT METRIC MANIFOLDS 149 158 EN Esmaeil Peyghan Hassan Nasrabadi Akbar Tayebi In this paper, we prove that evry 3-dimensional manifold M is a ∅-recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ∅-recurrent contact metric manifolds of constant curvature. This implies that there exists no ∅-recurrent N(k)-contact metric manifold, which is neither symmetric nor locally ∅-symmetric. No potential conflict of interest relevant to this article was reported.