Riemann solitons on \((\kappa, \mu)\)-almost cosymplectic manifolds. (English) Zbl 1523.53099
Summary: 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 \(\kappa < 0\).
MSC:
| 53E50 | Flows related to symplectic and contact structures |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53D15 | Almost contact and almost symplectic manifolds |
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