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Einstein-Weyl structures on almost cosymplectic manifolds. (arXiv:1801.05533v2 [math.DG] UPDATED)
来源于:arXiv
In this article, we study Einstein-Weyl structures on almost cosymplectic
manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-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
$\alpha$-cosymplectic manifold admitting closed Einstein-Weyl structures, we
prove that it is Ricc-flat. Further, we show that an almost
$\alpha$-cosymplectic admitting two Einstein-Weyl structures is either Einstein
or $\alpha$-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. 查看全文>>