The Boy-Gauss-Bonnet theorems for \(C^\infty\)-singular surfaces with limiting tangent bundle
type: Item
instance of: scholarly article
title: The Boy-Gauss-Bonnet theorems for \(C^\infty\)-singular surfaces with limiting tangent bundle
zbMATH Open document ID: 1006.53006
DOI: 10.1023/A:1014239727720
author: Marek Kossowski
published in: Annals of Global Analysis and Geometry
publication date: 2002-05-30T00:00:00Z
review text: The author investigates \(C^\infty\)-maps \(j\) of compact, oriented, smooth two dimensional manifolds \(M\) into the Euclidean three-space \(\mathbb{E}^3\) which are not immersions, i.e. where rank \(j_*<2\) for the critical locus \(D^0\subset M\). In order to get useful results he restricts himself to the case that there exists a \(C^\infty\)-global unit normal vector field of \(j(M)\). Further transversality assumptions are made for the points of \(D^0\) which imply that \(D^0\) is a disjoint union of \(C^\infty\)-embedded closed curves in \(M\). Then two global Gauss-Bonnet theorems are proved for the CW-complex \(j(M)\). Moreover applications for Weyl's tube formula and parallel surfaces are indicated.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 57N65
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 1747786
zbMATH Keywords: nonimmersive maps
zbMATH Keywords: global unit normal vector field
zbMATH Keywords: global Gauss-Bonnet theorems
reviewed by: Kurt Leichtweiß
MaRDI profile type: Publication
full work available at URL: a:1014239727720
OpenAlex ID: W62088312
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description: scientific article; zbMATH DE number 1747786