2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230283We 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 theoremDifferential Geometry53C17; 53B05, 53C05text