Volume 33 • Number 3 • 2010   • From the Eisenhart Problem to Ricci Solitons in ƒ-Kenmotsu Manifolds Constantin Calin and Mircea Crasmareanu Abstract. The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular ƒ-Kenmotsu framework. In this way, the Olszack-Rosca example of Einstein manifolds provided by ƒ-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some other classes of Einstein-Kenmotsu manifolds are presented. Our result is interpreted in terms of Ricci solitons and special quadratic first integrals. 2010 Mathematics Subject Classification: 53C40, 53C55, 53C12, 53C42. Full text: PDF