Fabrice Baudoin - Microlocal and Global Analysi...
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Fabrice Baudoin - Microlocal and Global Analysis, Interactions with Geometry
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 rst eigenvalue estimates for the sub-Laplacian.
Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal
Cliord structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of
those spaces in codimension more than 2. This is joint work with Erlend Grong, Gianmarco Molino and Luca Rizzi.