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Local invariants and geometry of the sub-Laplacian on H-type foliations

Irina Markina, Professor @ Department of Mathematics, UiB

 Local invariants and geometry of the sub-Laplacian on $H$-type foliations
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Speaker: Irina Markina, Professor @ Department of Mathematics, UiB

Abstract: Let (M,g) be a smooth, oriented, connected Riemannian manifold equipped with a Riemannian foliation with bundle-like complete metric g and totally geodesic leaves satisfying some additional symmetry conditions. The manifold is studied in the framework of sub-Riemannian geometry with bracket generating distribution transversal to the totally geodesic fibers. Equipping M with the Bott connection we find local invariants by studying the small-time asymptotics of the sub-Riemannanian heat kernel. We obtain the first three terms in the asymptotic expansion of the Popp volume for the pull-back of small sub-Riemannian balls. We address also the question of local isometry of M as a sub-Riemannian manifold and its tangent group.

 This is the joint work with W. Bauer, A. Laaroussi (Leibnitz University of Hannover, Germany), S. Vega-Molino (University of Bergen, Norway)

In spite that the abstract sound very technical, I will not go to details and will present only the main idea of the work, such that it would be accessible by master students.