Ricci solitons in almost $f$-cosymplectic manifolds

Abstract

In this article we study an almost f -cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic (κ, µ)-manifold. Further, we consider an almost f -cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector field and show that a three dimesional almost f -cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional η-Einstein almost f -cosymplectic manifold admitting a Ricci soliton.2010 Mathematics Subject Classification. 53D15; 53C21; 53C25.

Ricci Solitons and Certain Related Metrics on Almost Co-Kaehler Manifolds

“…They were also studied by Ghosh and Sharma [20], Calin and Crasmareanu [5], Ghosh [16], Turan et al [34], Crasmareanu [12], Cho [11], Ghosh [17], Bejan and Crasmareanu [2], Wang and Liu [40], Naik and Venkatesha [26,27], Venkatesha et al [35,36] and others. In the context of almost co-Kaehler manifolds, Ricci solitons were studied by Wang [38,39], Chen [10], Suh and De [32] and many others.…”