The groups of basic automorphisms of complete Cartan foliations
type: Item
instance of: scholarly article
title: The groups of basic automorphisms of complete Cartan foliations
zbMATH Open document ID: 1394.53035
DOI: 10.1134/S1995080218020245
author: K. I. Sheina
author: N. I. Zhukova
published in: Lobachevskii Journal of Mathematics
publication date: 2018-06-25T00:00:00Z
review text: A great deal of (regular) foliation theory may be modelled in terms of Cartan geometries, formulating the notion of a Cartan foliation. The objective of the paper under review is to provide sufficient conditions for the group of basic automorphisms of a complete Cartan foliation to admit the structure of a finite-dimensional Lie group. This is achieved using Molino's theorem regarding the closure of leaves of a complete Cartan foliation \((M,F)\). The authors consider two Lie algebras \(\mathfrak{g}_0(M,F)\) and \(\mathfrak{g}_1(M,F)\) arising from this theorem, and show that if \(\mathfrak{g}_0(M,F)\) vanishes then the above automorphism group for \((M,F)\) is a Lie algebra. Sharp upper bounds for the dimension of this group are given, using the transverse geometry of the foliation. Also, conditions are provided for this group to be discrete.
reviewed by: Iakovos Androulidakis
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 6893826
zbMATH Keywords: Cartan foliation
zbMATH Keywords: Lie group
zbMATH Keywords: basic automorphism
zbMATH Keywords: automorphism group
zbMATH Keywords: foliated bundle
MaRDI profile type: Publication
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full work available at URL: s1995080218020245
OpenAlex ID: W2727673288
description: scientific article; zbMATH DE number 6893826