Einstein-Weyl structures on trans-Sasakian manifolds

Abstract

Abstract In this article we study Einstein-Weyl structures on a 3-dimensional trans-Sasakian manifold M of type (α, β). First, we prove that a 3-dimensional trans-Sasakian manifold admitting both Einstein-Weyl structures W± = (g, ±θ) is Einstein, or is homothetic to a Sasakian manifold if α ≠ 0. Next for β ≠ 0 it is proved that M is Einstein, or is homothetic to an f-Kenmotsu manifold if it admits an Einstein-Weyl structure W = (g, κη) for some nonzero constant κ. Finally, a classification is obtained when a trans-Sasakian manifold admits a closed Einstein-Weyl structure. Further, if M is compact we also obtain two corollaries.