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Ricci Solitons on Almost Co-Kähler Manifolds
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 07 December 2018, pp. 912-922
- Print publication:
- December 2019
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- Article
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In this paper, we prove that if an almost co-Kähler manifold of dimension greater than three satisfying
$\unicode[STIX]{x1D702}$-Einstein condition with constant coefficients is a Ricci soliton with potential vector field being of constant length, then either the manifold is Einstein or the Reeb vector field is parallel. Let 
$M$ be a non-co-Kähler almost co-Kähler 3-manifold such that the Reeb vector field 
$\unicode[STIX]{x1D709}$ is an eigenvector field of the Ricci operator. If 
$M$ is a Ricci soliton with transversal potential vector field, then it is locally isometric to Lie group 
$E(1,1)$ of rigid motions of the Minkowski 2-space.
