2023/11/30 by Marini, Stefano, Tardini, Nicoletta, Zedda, Michela
#32H02 #32Q20 #53C25 #53C42 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.18754
Motivated by a conjecture in [9] we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to \mathcal Da-homothetic transformations, Kähler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the Kähler potentials of the transverse Kähler metric and of the cone metric.