Canonical connections on sub-Riemannian manifolds with constant symbol

2020/10/11 by Erlend Grong, Grong, Erlend · 1 citation
Computer Science · Mathematics · #17B70 #53C17 #58A15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2010.05366

openalex publication_date 2020/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a tool to address the equivalence problem in sub-Riemannian geometry, we introduce a canonical choice of grading and compatible affine connection, available on any sub-Riemannian manifold with constant symbol. We completely compute these structures for contact manifolds of constant symbol, including the cases where the connections of Tanaka-Webster-Tanno are not defined. We also give an original intrinsic grading on sub-Riemannian (2,3,5)-manifolds, and use this to present the first flatness theorem in this setting.

Citations

• A theorem on holonomy
• Affine connections and curvature in sub-Riemannian geometry

Cited by

• Effective normalization of sub-Riemannian connections

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