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Sub-Riemannian curvature in contact geometry

Agrachev, Andrey
•
Barilari, Davide
•
Rizzi, Luca
2017
  • journal article

Periodico
THE JOURNAL OF GEOMETRIC ANALYSIS
Abstract
We compare different notions of curvature on contact sub-Riemannian manifolds. In particular we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equation. The main result is that all these coefficients are encoded in the asymptotic expansion of the horizontal derivatives of the sub-Riemannian distance. We explicitly compute their expressions in terms of the standard tensors of contact geometry. As an application of these results, we prove a version of the sub-Riemannian Bonnet-Myers theorem that applies to any contact manifold, with special attention to contact Yang-Mills structures.
DOI
10.1007/s12220-016-9684-0
WOS
WOS:000394261100014
Archivio
http://hdl.handle.net/20.500.11767/11461
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84958779138
https://arxiv.org/abs/1505.04374
Diritti
closed access
Soggetti
  • Bonnet–Myer

  • Comparison

  • Contact

  • Curvature

  • Sub-Riemannian

  • Settore MAT/05 - Anal...

Scopus© citazioni
19
Data di acquisizione
Jun 2, 2022
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Web of Science© citazioni
17
Data di acquisizione
Mar 21, 2024
Visualizzazioni
4
Data di acquisizione
Apr 19, 2024
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