A Bonnet–Myers type theorem for quaternionic contact structures

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 tens...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2019-02, Vol.58 (1), p.1-26, Article 37
Hauptverfasser:	Barilari, Davide, Ivanov, Stefan
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Calculus of Variations and Optimal Control Optimization Control Mathematical and Computational Physics Mathematics Mathematics and Statistics Systems Theory Tensors Theorems Theoretical
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Zusammenfassung:	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.
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-018-1467-y