A topological proof of the Arnold four cusps theorem
type: Item
instance of: scholarly article
title: A topological proof of the Arnold four cusps theorem
zbMATH Open document ID: 1252.58008
published in: Bulletin of the London Mathematical Society
publication date: 2012-08-08T00:00:00Z
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6064188
zbMATH Keywords: generic surface
zbMATH Keywords: Whitney cusp
zbMATH Keywords: elliptic metric
zbMATH Keywords: bending angle
zbMATH Keywords: caustic
zbMATH Keywords: semi-cubical vertice
author: V. A. Vassiliev
MaRDI profile type: Publication
full work available at URL: bdr119
OpenAlex ID: W2106873824
DOI: 10.1112/BLMS/BDR119
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review text: \textit{V. I. Arnold} in [Rev. Mat. Univ. Complutense Madr. 8, No. 1, 109--119 (1995; Zbl 0973.53501)] proved a theorem stating that on a generic Riemannian surface which is sufficiently close to a sphere has at least four semi-cubical vertices. The author proves the same fact using the Morse theory and replacing the condition of closeness to the sphere by some less restrictive geometric hypothesis.
reviewed by: Witold Mozgawa
description: scientific article; zbMATH DE number 6064188