The Gauss-Bonnet-Grotemeyer theorem in space forms
type: Item
instance of: scholarly article
title: The Gauss-Bonnet-Grotemeyer theorem in space forms
zbMATH Open document ID: 1208.53059
author: Eric L. Grinberg
author: Haizhong Li
published in: Inverse Problems and Imaging
publication date: 2011-01-17T00:00:00Z
review text: Let \(M\) be an oriented closed surface in the \(3\)-dimensional Euclidean space \(\mathbb R^3\) with Gauss curvature \(G\) and unit vector field \({\vec{n}}\). By replacing the Gauss curvature \(G\), with \(({\vec{a}\cdot {\vec{n}}})^2G\), where \({\vec{a}}\) is a fixed unit vector field, \textit{K. P. Grotemeyer} extended the well-known Gauss-Bonnet theorem [Ann. Acad. Sci. Fenn., Ser. A I 336, No. 15 (1963; Zbl 0117.38401)]. In this paper, the authors generalize Grotemeyer's result to oriented closed even-dimensional hypersurfaces of dimension \(n\) in an \((n+1)\)-dimensional space form \(N^{n+1}(k)\)
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 5837979
zbMATH Keywords: Gauss-Bonnet theorem
zbMATH Keywords: Gauss-Kronecker curvature
zbMATH Keywords: hypersurfaces
zbMATH Keywords: Grotemeyer
MaRDI profile type: Publication
full work available at URL: ipi.2010.4.655
OpenAlex ID: W2316560026
DOI: 10.3934/IPI.2010.4.655
description: scientific article; zbMATH DE number 5837979