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A Bonnet–Myers type theorem for quaternionic contact structures

  • Davide BarilariEmail author
  • Stefan Ivanov
Article
  • 16 Downloads

Abstract

We prove a Bonnet–Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms of derivatives up to the third order of the fundamental tensors, then the manifold is compact and we give a sharp bound on its sub-Riemannian diameter.

Mathematics Subject Classification

53C17 53D25 

Notes

Acknowledgements

The first author has been supported by the ANR project SRGI “Sub-Riemannian Geometry and Interactions”, Contract Number ANR-15-CE40-0018. The second author has been partially supported by Contract DH/12/3/12.12.2017 and Contract 195/2016 with the Sofia University “St.Kl.Ohridski”.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR CNRS 7586Université Paris-DiderotParis Cedex 13France
  2. 2.Faculty of Mathematics and InformaticsUniversity of SofiaSofiaBulgaria
  3. 3.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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