Holonomy of K-contact sub-Riemannian manifolds

Abstract: Given a contact sub-Riemannian manifold (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, which defines parallel transport of vectors tangent to D along curves tangent to D. The holonomy group of this connection is called the horizontal holonomy group. The adapted connection is an extension of the horizontal connection 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 one), the holonomy of the adapted connection is the holonomy of some Riemannian manifold, and the horizontal holonomy either coincides with the holonomy of the adapted connection, or it is a codimension-one normal subgroup of the later group. I will discuss the question of existence of parallel horizontal spinors, examples, and consequences.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.