Viernes 14/03/2025, 14:30 hs. Aula 27
Titulo: Homogeneous 3-(α, δ)-Sasaki manifolds and submersions onto quaternionic Kähler spaces
Resumen:
3-Sasaki manifolds are a very well-studied, but unfortunately rather rigid class of almost 3-contact metric manifolds (for example, they are always Einstein).
We define and investigate a new class of almost 3- contact metric manifolds depending on two real parameters, called 3-(α, δ)-Sasaki manifolds (including as special cases 3-α-Sasaki manifolds, quaternionic Heisenberg groups, and many others). We show that every 3-(α, δ)-Sasaki manifold of dimension 4n + 3 admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature 16n(n + 2)αδ and a canonical connection with skew torsion. In the non-degenerate case we describe all homogeneous 3-(α, δ)-Sasaki manifolds fibering over symmetric Wolf spaces and their non-compact dual symmetric spaces. This approach can be used to give a new proof of the classification of homogeneous 3-Sasaki manifolds purely in terms of root data of simple Lie groups.
This is joint work with Giulia Dileo (University of Bari, Italy) and Leander Stecker (Universität Leipzig, Germany)