Calculus of Variations and Geometric Measure Theory
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F. Baudoin - E. Grong - G. Molino - L. Rizzi

H-type foliations

created by rizzi1 on 07 Dec 2018

[BibTeX]

Preprint

Inserted: 7 dec 2018
Last Updated: 7 dec 2018

Year: 2018

ArXiv: 1812.02563 PDF

Abstract:

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound, we prove on those structures sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of those spaces in codimension more than 2.

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