RIEMANN SOLITONS ON (κ, μ)-ALMOST COSYMPLECTIC MANIFOLDS

In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on (kappa, mu)-almost cosymplectic manifold M with kappa < 0 and we show that the soliton is expanding with lambda = kappa/2n-1 (4n - 1) and M is locally isometric to the Lie group G(rho). Finally, we prove the non-existence of gradient almost Riemann soliton on a (kappa, mu)-almost cosymplectic manifold of dimension greater than 3 with kappa < 0.