Canonical connections on sub-Riemannian manifolds with constant symbol

Key Points

• This study aims to establish a canonical grading and affine connection for sub-Riemannian manifolds with constant symbol.
• Introduced a canonical grading based on Morimoto’s normalization conditions.
• Computed structures for contact manifolds of constant symbol.
• Developed an intrinsic grading for sub-Riemannian (2,3,5)-manifolds.
• Presented the first flatness theorem in this setting.
• Defined a new canonical choice of grading applicable to various sub-Riemannian manifolds.
• Computed structures for contact manifolds even when Tanaka-Webster-Tanno connections are undefined.
• Demonstrated the first flatness theorem for the proposed manifold setting.

Abstract