2019/09/02 by Xiaomin Chen, Chen, Xiaomin
Mathematics · #53C25 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1909.00758
openalex publication_date 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures (g, V, m, λ). First we prove that an almost cosymplectic (κ,μ)-manifold is locally isomorphic to a Lie group if (g, V, m, λ) is closed and on a compact almost (κ,μ)-cosymplectic manifold there do not exist quasi-Einstein structures (g, V, m, λ), in which the potential vector field V is collinear with the Reeb vector filed ξ. Next we consider an almost α-cosymplectic manifold admitting a quasi-Einstein structure and obtain some results. Finally, for a K-cosymplectic manifold with a closed, non-steady quasi-Einstein structure, we prove that it is η-Einstein. If (g, V, m, λ) is non-steady and V is a conformal vector field, we obtain the same conclusion.