Taut contact circles on H-contact 3-manifolds

Abstract

We classify non-Sasakian H-contact 3-manifolds (M, η, g) with (η, η1) taut contact circle (or, equivalently, Cartan structure), where η1 is a suitable 1-form orthogonal to η. In particular, a compact 3-manifold admits a taut contact circle if and only if it admits a non-Sasakian Hcontact metric structure satisfying ∇ξτ = 0, where ξ is the characteristic vector field and τ := Lξg is the torsion tensor.