Affine submanifolds and the theorem of Cartan-Ambrose-Hicks.
type: Item
instance of: scholarly article
title: Affine submanifolds and the theorem of Cartan-Ambrose-Hicks.
zbMATH Open document ID: 1065.53021
author: Knut Pawel
author: Helmut Reckziegel
published in: Kodai Mathematical Journal
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1071674466
review text: In this article E. Cartan's theorem on the existence of submanifolds with prescribed tangent space is generalized to manifolds equipped with a linear connection. Generalizations of this type -- in the local and global context -- have been considered by \textit{N. Hicks} [Ill. J. Math. 10, 661--679 (1966; Zbl 0184.25203)]; but Hicks had to make additional unpleasant assumptions to be satisfied. The authors succeed in omitting these assumptions and are able to reprove the theorem of Cartan-Ambrose-Hicks as a special case of their results. Moreover, the results are for manifolds of different dimensions and arbitrary rank of the affine map.
reviewed by: Martin Wiehe
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1910506
zbMATH Keywords: affine submanifolds
zbMATH Keywords: affine immersions
zbMATH Keywords: geodesically clomplete
MaRDI profile type: Publication
OpenAlex ID: W1970083732
DOI: 10.2996/KMJ/1071674466
description: scientific article; zbMATH DE number 1910506