On isomorphic classical diffeomorphism groups. III
type: Item
instance of: scholarly article
title: On isomorphic classical diffeomorphism groups. III
zbMATH Open document ID: 0832.53026
DOI: 10.1007/BF01120327
author: Augustin Banyaga
author: Andrew McInerney
published in: Annals of Global Analysis and Geometry
publication date: 1995-08-02T00:00:00Z
review text: [For part II see the first author, J. Differ. Geom. 28, No. 1, 23-35 (1988; Zbl 0645.53019)]. In this note the main result is the following theorem: Let \((M_i, \alpha_i)\), \(i = 1, 2\), be two paracompact, connected, smooth manifolds of dimension \(2n + 1\) equipped with contact forms \(\alpha_i\). If \(G_{\alpha_1} (M_1) \to G_{\alpha_2} (M_2)\) is a group isomorphism, then there exists a unique diffeomorphism \(w : M_1 \to M_2\) such that for all \(h \in G_{\alpha_1} (M_1)\), \(\phi (h) = whw^{-1}\) and \(w^*\alpha_2 = \lambda \alpha_1\), for some nowhere vanishing function \(\lambda\) (i.e., the contact structures are determined by their automorphism groups).
reviewed by: Nicolae A. Soare
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 780910
zbMATH Keywords: isomorphic diffeomorphism groups
zbMATH Keywords: contact structures
zbMATH Keywords: automorphism groups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01120327
OpenAlex ID: W3158117863
description: scientific article; zbMATH DE number 780910