Taut contact circles and bi-contact metric structures on three-manifolds (Q2407996)

The author studies the taut contact metric circles on Riemannian manifolds and bi-contact metric structures. A pair \((\eta_1,\eta_2)\) of contact 1-forms on a three-manifold is called a contact circle if for every \(a=(a_1,a_2)\in S^1\) the linear combination \(\eta_a=a_1\eta_1+a_2\eta_2\) is also a contact form. A contact circle \((\eta_1,\eta_2)\) is said to be a taut contact circle if the volume forms \(\eta_a\wedge d\eta_a\) are equal for every \(a\in S^1\). A taut contact metric circle on a three-manifold is a triple \((\eta_1,\eta_2,g)\) where \((\eta_1,\eta_2)\) is a taut contact circle and \(g\) is an associated metric to both of the contact forms \(\eta_1,\eta_2\). The author also defines the notion of bi-contact metric structure on a three-manifold \(M\). He investigates the existence of taut contact metric circles and bi-H-contact metric structures. The classification of simply connected three-manifolds admitting a bi-H-contact metric structure is given.