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<p>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. This grading and affine connection is based on Morimoto’s normalization conditions in [<CitationRef CitationID="CR30">30</CitationRef>]. 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.</p>

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Canonical connections on sub-Riemannian manifolds with constant symbol

  • 期刊论文

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  • 发表日期：

    2026年2月11日

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  • Erlend Grong

摘要

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. This grading and affine connection is based on Morimoto’s normalization conditions in [30]. 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.