A construction of Kähler-Einstein metrics using Galois coverings, studied by ArezzoGhigi-Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of ℂℙn which are trivial set theoretically, one obtains new Einstein metrics on odd-dimensional spheres. The method also gives Kähler-Einstein metrics on degree 2 Del Pezzo surfaces with A1- or A2-singularities.
All Science Journal Classification (ASJC) codes
- Einstein metrics
- Exotic spheres
- Kähler-Einstein orbifolds
- Sasakian manifolds