On \(\phi\)-recurrent generalized \((k,\mu)\)-contact metric manifolds (Q2470028)

The paper introduces the notion of locally \(\varphi\)-recurrent \((k,\mu)\)-contact metric manifold and locally \(\varphi\)-recurrent generalized \((k,\mu)\)-contact metric manifold by extending definitions and results given by \textit{A. A. Shaikh}, \textit{K. Arslan}, \textit{C. Murathan} and \textit{K. K. Baishya} [Balkan J. Geom. Appl. 12, No. 1, 122--134 (2007; Zbl 1135.53019)] in case of locally \(\varphi\)-symmetric \((k,\mu)\)-contact metric manifolds. The authors deal with the 3-dimensional case as \textit{T. Koufogiorgos} and \textit{C. Tsichlias} [Can. Math. Bull. 43, No. 4, 440--447 (2000; Zbl 0978.53086)] proved the existence of generalized \((k,\mu)\)-contact metric manifold only for dimension 3. Furthermore, they describe a non trivial example pointing out the existence of such metric manifolds.