Manifolds modelled over free modules over the double numbers
type: Item
instance of: scholarly article
title: Manifolds modelled over free modules over the double numbers
zbMATH Open document ID: 1049.58002
DOI: 10.1023/A:1025037325005
author: Joseph Grifone
author: Jaime Muñoz Masqué
author: P. M. Gadea
published in: Acta Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: Let \(\mathbb B:=\{z=x+jy\mid x,y\in \mathbb R,\;j^2=1\}\) be the algebra of double numbers. The authors introduce and study the concept of \(\mathbb B\)-differentiability, \(\mathbb B\)-analyticity and \(\mathbb B\)-holomorphy of a map \(F:U\to \mathbb B\) where \(U\subset \mathbb B^n\) is an open set. Next they turn to \(\mathbb B\)-manifolds and derive an important criterion for a \(2n\)-dimensional non-integrable \(\mathbb B\)-manifold to be a \(\mathbb B\)-manifold.
Mathematics Subject Classification ID: 58A05
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 2098987
zbMATH Keywords: B-analycity
zbMATH Keywords: B-holomorphy
zbMATH Keywords: manifolds over the double numbers
zbMATH Keywords: equidimensional supplementary foliations
reviewed by: József Szilasi
MaRDI profile type: Publication
full work available at URL: a:1025037325005
OpenAlex ID: W1809165453
description: scientific article; zbMATH DE number 2098987