A canonical connection on sub-Riemannian contact manifolds

TL;DR

This paper introduces a new canonical affine connection for sub-Riemannian contact manifolds, inspired by the Levi-Civita connection, and compares it with existing Tanaka-Webster connections in three dimensions.

Contribution

It constructs a canonical affine connection in sub-Riemannian contact geometry, providing a new tool analogous to Levi-Civita in Riemannian geometry.

Findings

The connection is canonically defined for sub-Riemannian contact manifolds.

Comparison with Tanaka-Webster connection in 3D shows similarities and differences.

The method mimics Levi-Civita construction in a sub-Riemannian setting.

Abstract

We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.