7 sep 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminari di Geometria del Dini
Abstract.
The third Betti number of a compact homogeneous space M=GK, where G has s simple factors and dim(K)>0, is always less or equal than s-1. Equality holds if and only if certain s-vectors defined by the Killing constants are all collinear and in that case, M=GK is called aligned. In this talk, we will give formulas for the Ricci curvature of G-invariant metrics on aligned homogeneous spaces with s=2 and present two applications:
1) New examples of generalized Einstein metrics (or Bismut Ricci flat generalized metrics (g,H), i.e., the fixed points of the generalized Ricci flow studied by Garcia-Fernandez and Streets), as a generalization of results by Podestà and Raffero.
2) New examples of Einstein metrics in the largely unexplored case of compact homogeneous spaces GK with G non-simple.