descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2013 English Publisher:Oxford University Press (OUP)Journal:International Mathematics Research Notices, volume 2,015, pages 13,290-13,323 (issn: 1073-7928, eissn: 1687-0247,

Authors: Daniel, Jeremy; Ma, Xiaonan;

doi: 10.1093/imrn/rnv104 , 10.48550/arxiv.1304.4808

arXiv: 1304.4808

Characteristic Laplacian in Sub-Riemannian Geometry

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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.

Related Organizations

University of Paris
France
Paris Diderot University
France

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

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