Connections on infinite-dimensional manifolds with corners
type: Item
instance of: scholarly article
title: Connections on infinite-dimensional manifolds with corners
zbMATH Open document ID: 0898.53022
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-10-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108444
review text: This paper extends the study of infinite dimensional manifolds with corners, see, e.g., the earlier works by the authors [\textit{S. Armas-Gómez, J. Margalef Roig, E. Outerelo-Domínguez} and \textit{E. Padrón-Fernández}, Rend. Circ. Mat. Palermo, II. Ser. 44, 45-93 (1995; Zbl 0833.58007); the last three authors, Acta Math. Hung. 72, 105-119 (1996; Zbl 0865.58004)]. The connections on general fiber bundles and vector bundles over such manifolds are the main theme here. About one half of the paper is devoted to the exposition of basic categorical constructions with such bundles; then various types of connections are discussed. As usual in theories including infinite dimensional manifolds, the exposition must be as much coordinate free as possible and then most of the standard features from the finite dimensional cases can be recovered for Banach spaces. The existence theorems are often exceptions, though. The authors prove the existence of linear connections and principal connections at the end of their paper.
reviewed by: Jan Slovák
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 58B10
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 57R22
Mathematics Subject Classification ID: 58E40
Mathematics Subject Classification ID: 55R05
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 1115650
zbMATH Keywords: manifolds with corners
zbMATH Keywords: connections
zbMATH Keywords: manifolds modelled on Banach spaces
author: Juan Margalef
author: Enrique Outerelo
author: E. Padrón- Fernández
MaRDI profile type: Publication
cites work: Q4277803
cites work: Q4693714
cites work: Q5649693
cites work: Parallélismes
cites work: Q4273372
cites work: Q4003971
cites work: Q5288267
cites work: Principal bundles on infinite dimensional manifolds with corners
cites work: Q3871594
cites work: Connections on tangent bundles
description: scientific article; zbMATH DE number 1115650