A Natural Connection on (2,3) Sub-Riemannian Manifolds

Abstract

We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.

14 pages, no figures. Fixed a small error in the main theorem

References in corpus (2)

• Constant mean curvature surfaces in sub-Riemannian geometry
• Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model