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arXiv · 1006.3132

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

Constantin Călin·Mircea Crasmareanu
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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.

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Constantin Călin, Mircea Crasmareanu. 2010-06-16. From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds. https://arxiv.org/abs/1006.3132

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