Existence and non-existence of constant scalar curvature and extremal Sasaki metrics (Q6165546)

This paper is a fundamental work on the theory of extremal Sasakian metrics. Several aspects of the problem of the existence and non-existence of constant scalar curvature (CSC) Sasakian metrics are studied. It is proved that the natural Sasaki-Boothby-Wang manifold over the admissible projective bundles over local products of non-negative CSC Kähler metrics always has a CSC Sasakian metric in its so-called Sasaki-Reeb cone. The authors present two families of examples of complex cones for which the extremal Sasaki-Reeb cone has interesting properties.