Isometric immersions of closed manifolds of nonnegative curvature
type: Item
instance of: scholarly article
title: Isometric immersions of closed manifolds of nonnegative curvature
zbMATH Open document ID: 1009.53044
DOI: 10.1023/A:1015362631423
author: N. D. Lebedeva
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-08-29T00:00:00Z
review text: The author extends a result of \textit{S. Z. Shefel}' [Sib. Mat. Zh. 10, 459-466 (1969; Zbl 0174.53101)] by proving that if \(M\) is a closed \(n\)-manifold and \(f:M\to \mathbb{R}^N\) an immersion inducing a \(C^2\)-smooth (or polyhedral) metric of nonnegative curvature on \(M\), and such that this nonnegativity property is preserved under composition with all affine transformations of \(\mathbb{R}^N\), then \(f\) is an embedding and \(f(M)\) is a \(C^2\)-smooth convex body (or polyhedron) in \(\mathbb{R}^{n+1}\).
reviewed by: G. Tarantello
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1777776
zbMATH Keywords: induced metric
zbMATH Keywords: immersion
zbMATH Keywords: affine transformations
zbMATH Keywords: convex body
MaRDI profile type: Publication
full work available at URL: a:1015362631423
OpenAlex ID: W12957111
description: scientific article; zbMATH DE number 1777776