2018/01/17 by Xiaomin Chen, Chen, Xiaomin
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1801.05533
In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic (κ,μ)-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost α-cosymplectic manifold admitting closed Einstein-Weyl structures, we prove that it is Ricc-flat. Further, we show that an almost α-cosymplectic admitting two Einstein-Weyl structures is either Einstein or α-cosymplectic, provided that its Ricci tensor is commuting. Finally, we prove that a compact K-cosymplectic manifold with a closed Einstein-Weyl structure or two special Einstein-Weyl structures is cosymplectic.