On a Carathéodory's conjecture on umbilics: representing ovaloids
type: Item
instance of: scholarly article
title: On a Carathéodory's conjecture on umbilics: representing ovaloids
zbMATH Open document ID: 0897.53003
author: J. Ning
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-10-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108443
review text: Carathéodory's conjecture states that every ovaloid in Euclidean 3-space has at least two umbilics. Apparently, this can now be considered to be proved in the analytic case, but the \(C^r\) case is still open. In this connection, the authors consider representations of ovaloids. For the so-called Bonnet chart they give the differential equation of the curvature lines. The support function, defined on \(S^2\), is arbitrarily extended to a neighborhood of \(S^2\). An explicit formula gives the points of the ovaloid in terms of such an extension.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 53C45
zbMATH DE Number: 1115661
zbMATH Keywords: stereographic projection
zbMATH Keywords: Carathéodory's conjecture
zbMATH Keywords: umbilics
zbMATH Keywords: representations of ovaloids
zbMATH Keywords: Bonnet chart
zbMATH Keywords: curvature lines
zbMATH Keywords: support function
reviewed by: Erhard Heil
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1115661