Un panorama de variedades aproximadamente Kähler.
Si dimostra l'esistenza di una struttura complessa compatibile globale sulle varietà quaternionali di Hermite-Weyl compatte regolari. Se ne deducono alcune restrizioni sui numeri di Betti.
The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.
As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.