Extremal Sasakian geometry on \(S^{3}\)-bundles over Riemann surfaces (Q2929651)

As an extension of [the authors, Afr. Diaspora J. Math. 14, No. 2, 98--117 (2012; Zbl 1285.53034)], the authors investigate the existence of extremal Sasaki metrics on \(S^3\)-bundle, over a Riemann surface of genus \(g>0\). They prove the existence of a countably infinite number of inequivalent contact structures on the total space of the considered bundles, which admits 2D Sasaki cones, each with a Sasaki metrics of constant scalar curvature. Studying the extremal subset in the Sasaki cone, they obtain that it exhausts the entire cones, under the assumption \(0<g\leq4\).