We discuss the existence and non-existence of constant scalar curvature, as well extremal, Sasaki metrics. prove that natural Sasaki–Boothby–Wang manifold over admissible projective bundles local products non-negative CSC Kähler metrics, described in [3], always has a curvature (CSC) metric its Sasaki-Reeb cone. Moreover, we give examples show extremal Sasaki–Reeb cone, defined set vector field...