The paper explores existence and non-existence of constant scalar curvature and extremal Sasaki metrics.
problem Existence and non-existence of constant scalar curvature and extremal Sasaki metrics.
method Analyzing natural Sasaki-Boothby-Wang manifolds and extremal Sasaki metrics on admissible projective bundles.
result The extremal Sasaki--Reeb cone is not necessarily connected and can be empty even in the non-Gorenstein case.