From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds

Abstract

The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular $f$-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by $f$-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.

12 pages

References in corpus (1)

• Ricci solitons in contact metric manifolds

Cited by in corpus (8)

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• Almost Ricci-like solitons with torse-forming vertical potential of constant length on almost contact B-metric manifolds
• Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold
• Almost $\eta$-Ricci solitons in $(LCS{)}_n$-manifolds
• Ricci solitons in manifolds with quasi-constant curvature
• Solitonic aspects of submanifolds in Kenmotsu statistical manifolds
• Characteristics of conformal Ricci soliton on warped product spaces