A note on almost Riemann Solitons and gradient almost Riemann Solitons

The object of the offering article is to investigate an almost Riemann soliton and a gradient almost Riemann soliton in a non-cosymplectic normal almost contact metric manifold M-3. Before all else, it is proved that if the metric of M-3 is a Riemann soliton with divergence-free potential vector field Z, then the manifold is quasi-Sasakian and is of constant sectional curvature -lambda, provided alpha, beta = constant. Also, it is shown that if the metric of M-3 is an almost Riemann Soliton and Z is pointwise collinear with. and has constant divergence, then Z is a constant multiple of xi and the almost Riemann Soliton reduces to a Riemann soliton, provided alpha, beta =constant. Additionally, it is established that if M-3 with alpha, beta = constant admits a gradient almost Riemann soliton (gamma, xi, lambda), then the manifold is either quasi-Sasakian or is of constant sectional curvature -(alpha(2) - beta(2)). Finally, we develop an example of M-3 admitting a Riemann soliton.