The Horizontal Einstein Property for H-Type sub-Riemannian Manifolds

manifolds
Grenoble
[MATH]Mathematics [math]
sub-riemannian
sous-riemannien
sub-riemannian days 2018
journées sous-riemanniennes 2018
H-Type
horizontal Einstein property

Appears in collection : Journée sous-riemannienne 2018

We generalize the notion of H-type sub-Riemannian manifolds introduced by Baudoin and Kim, and then introduce a notion of parallel Clifford structure related to a recent work of Moroianu and Semmelmann. On those structures, we prove an Einstein property for the horizontal distribution using ideas from Ishihara’s work on hyper-Kahler and bquaternionic Kahler manifolds. This is a joint work with F. Baudoin, E. Grong, and L. Rizzi.