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arXiv · 1807.06815

Riemannian metrics and Laplacians for generalised smooth distributions

Iakovos Androulidakis·Yuri Kordyukov
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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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BibTeXRIS

Iakovos Androulidakis, Yuri Kordyukov. 2018-07-18. Riemannian metrics and Laplacians for generalised smooth distributions. https://arxiv.org/abs/1807.06815

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