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Ricci Solitons on Almost Co-Kähler Manifolds

  • Yaning Wang (a1)

Abstract

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.

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This work was supported by Youth Science Foundation of Henan Normal University (No. 2014QK01).

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Ricci Solitons on Almost Co-Kähler Manifolds

  • Yaning Wang (a1)

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