On global hypoellipticity of horizontal Laplacians on compact principal bundles
type: Item
instance of: scholarly article
title: On global hypoellipticity of horizontal Laplacians on compact principal bundles
zbMATH Open document ID: 0734.58047
author: Hideki Omori
published in: Hokkaido Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: Let M be a smooth, Riemannian, connected manifold without boundary and let \(X_ 1,X_ 2,...,X_ k\) be finitely many smooth vector fields on M. The author states the following conjecture: A differential operator \(L=\sum X^*_ iX_ i\) is globally hypoelliptic if the group generated by \(\{\) exp \(\sum f_ iX_ i\); \(f_ i\in C^{\infty}(M)\}\) acts transitively on M. This conjecture is affirmative in the real analytic case because of the Hörmander theorem. In the paper the case of horizontal Laplacian on compact principal bundles is considered and a characterization of its global hypoellipticity is given.
Mathematics Subject Classification ID: 58J99
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 4215008
zbMATH Keywords: horizontal Laplacian
zbMATH Keywords: principal bundles
zbMATH Keywords: global hypoellipticity
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413838
OpenAlex ID: W2054371217
DOI: 10.14492/HOKMJ/1381413838
description: scientific article; zbMATH DE number 4215008