On umbilic points on newly Born surfaces
type: Item
instance of: scholarly article
title: On umbilic points on newly Born surfaces
zbMATH Open document ID: 1387.53010
author: Masaru Hasegawa
author: Farid Tari
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2018-01-16T00:00:00Z
review text: The authors show that newly born surfaces in 3-space have 4 and only 4 umbilic points. Umbilics are points on a surface where the curvature is the same in any direction. That is, locally, the surface is spherical. Here, a newly born surface is characterized as a surface created from a function with Morse singularity of index either 0 or 3. In addition to the main proof, the authors further show all 4 umbilic points are of lemon type.
reviewed by: James P. Howard II
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 6826670
zbMATH Keywords: umbilic points
zbMATH Keywords: surfaces
zbMATH Keywords: singularities
zbMATH Keywords: lines of principal curvature
MaRDI profile type: Publication
full work available at URL: s00574-017-0037-9
OpenAlex ID: W2612369742
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Wikidata QID: Q125852529
DOI: 10.1007/S00574-017-0037-9
description: scientific article; zbMATH DE number 6826670