Riemann solitons on $(\kappa, \mu)$-almost cosymplectic manifolds
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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 $\kappa < 0$.
Abstract
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 $\kappa < 0$.
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