On Calabi's diastasis function of the cigar metric
  We show that the Cigar metric on $\mathbb{C}$ is an example of real analytic K\"ahler manifold with globally defined and positive Calabi's diastasis function which cannot be K\"ahler immersed into any (finite or infinite dimensional) complex space form. 
Andrea Loi, Michela Zedda
math.DG math.CV