Communications of the
Korean Mathematical Society CKMS

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 $\lambda = \frac{\kappa}{2n-1}(4n-1)$ 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 $\kappa < 0$.

Keywords: Riemann soliton, almost cosymplectic manifold

MSC numbers: 53C25, 53C25, 53D15

Supported by: The author Amruthalakshmi M. R., is thankful to Department of Science and Technology, Ministry of Science and Technology, Government of India, for providing financial assistance through DST INSPIRE Fellowship (No: DST/INSPIRE Fellowship/[IF 190869]).