Abstract
Let M3 be a 3-dimensional contact metric manifold with contact structure (φ, ξ, η, g), such thatφ and ℓ=R(.,ξ)ξ) commute. Such a manifold is called 3-τ-manifold. We prove that every 3-τ-manifold with η-parallel Weyl tensor is either flat or a Sasakian manifold with constant curvature 1.
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Gouli-Andreou, F., Xenos, P.J. On a class of 3-dimensional contact metric manifolds. J Geom 63, 64–75 (1998). https://doi.org/10.1007/BF01221239
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DOI: https://doi.org/10.1007/BF01221239