Document Type : Original Article
Department of Mathematics, The University of Burdwan, Golapbag, Burdwan – 713104, West Bengal, India.
Department of Mathematics, Poornima College of Engineering, ISI-6, RIICO Institutional Area, Sitapura, Jaipur – 302022, Rajasthan, India.
Department of Mathematics, Govt. College of Engineering and Technology, Berhampur, Murshidabad – 742101, West Bengal, India.
The object of the present paper is to study the $\phi $-Ricci symmetric, locally $\phi $-Ricci symmetric and cyclic Ricci parallel three-dimensional $f$-Kenmotsu manifold bearing the function $f$ being constant. We have considered almost conformal Ricci soliton on the three-dimensional $f$-Kenmostu manifold and deduced the condition for an almost conformal Ricci soliton, which becomes conformal Ricci soliton. Finally, examples on three-dimensional $f$-Kenmotsu manifold depending on nature of $f$ are constructed to illustrate the results.