Natural \(\mathrm{SU}(2)\)-structures on tangent sphere bundles (Q2004316)

For a given oriented Riemannian 3-manifold \(M\), the author defines and studies natural \(\mathrm{SU}(2)\)-structures, in the sense of Conti-Salamon, on the total space \(\mathcal{S}\) of the tangent sphere bundle of \(M\). Two types of structures arise: the contact-hypo and the non-contact and, for each of them, he studies the conditions for being hypo, nearly-hypo or double-hypo. New double-hypo structures on \(\mathbb{S}^3\times \mathbb{S}^2\) are discovered, of which the well-known Sasaki-Einstein are a particular case. Hyperbolic geometry examples also appear.