Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665712015ON ∅-RECURRENT CONTACT METRIC MANIFOLDS149158ENEsmaeilPeyghanHassanNasrabadiAkbarTayebiIn 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.