Riemannian metrics and Laplacians for generalised smooth distributions

2018/07/18 by Androulidakis, Iakovos, Kordyukov, Yuri
#35H10 #35R01 (Secondary) #53C17 #58A30 #58J60 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.06815

Abstract

We show that any generalised smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation which includes the distribution, we prove hypoellipticity.

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