• Corpus ID: 254247087

Tangent groupoid and tangent cones in sub-Riemannian geometry

@inproceedings{Mohsen2022TangentGA,
  title={Tangent groupoid and tangent cones in sub-Riemannian geometry},
  author={Omar Mohsen},
  year={2022}
}

• Omar Mohsen
• Published 3 December 2022
• Mathematics

Let X 1 , ¨ ¨ ¨ , X m be vector fields satisfying Hörmander’s Lie bracket generating condition on a smooth manifold M . We generalise Connes’s tangent groupoid, by constructing a com-pletion of the space M ˆ M ˆ R ˆ` using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorff distance. This generalises a result of Bellaïche.