On the differential geometry of frame bundles of Riemannian manifolds.

Kam-Ping Mok

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Curvature and the equivalence problem in sub-Riemannian geometry

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These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples,...