Characteristic Laplacian in sub-Riemannian geometry

2013/04/17 by Jeremy Daniel, Daniel, Jeremy, Xiaonan Ma +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1304.4808

arxiv created 2013/04/17 · arxiv updated 2013/04/18

Abstract

We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms in a complex setting. We also discuss the consequences of these negative results for a conjecture of P. Griffiths, concerning the characteristic cohomology of period domains.

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