BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anton Galaev (Hradec-Králové University) DTSTART:20251029T123000Z DTEND:20251029T133000Z DTSTAMP:20260502T044728Z UID:PHK-cohomology-seminar/139 DESCRIPTION:Title: Holonomy of K-contact sub-Riemannian manifolds\nby An ton Galaev (Hradec-Králové University) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\n\nLectu re held in ZOOM meeting.\n\nAbstract\nGiven a contact sub-Riemannian manif old (M\, θ\, g)\, where θ is a contact form on M\, and g is a metric on the contact distribution D = ker θ\, there is the Schouten connection\, w hich defines parallel transport of vectors tangent to D along curves tange nt to D. The holonomy group of this connection is called the horizontal ho lonomy group. The adapted connection is an extension of the horizontal con nection to a connection on the vector bundle D over M. I will show that in the K-contact case (which means that the Reeb vector field is a Killing o ne)\, the holonomy of the adapted connection is the holonomy of some Riema nnian manifold\, and the horizontal holonomy either coincides with the hol onomy of the adapted connection\, or it is a codimension-one normal subgro up of the later group. I will discuss the question of existence of para llel horizontal spinors\, examples\, and consequences.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/139/ END:VEVENT END:VCALENDAR