Almost Ricci solitons and K-contact geometry

We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric (g) is (K) -contact and flow vector field (X) is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for (X) strict, (g) becomes compact Sasakian Einstein.