An isolated umbilical point of the graph of a homogeneous polynomial
type: Item
instance of: scholarly article
title: An isolated umbilical point of the graph of a homogeneous polynomial
zbMATH Open document ID: 0980.53005
DOI: 10.1023/A:1005182230528
author: Naoya Ando
published in: Geometriae Dedicata
publication date: 2002-03-06T00:00:00Z
review text: Consider a homogeneous polynomial \(f\) in two real variables \(x,y\) of degree \(k\geq 3\) whose graph \((x,y,f(x,y))\) in \(\mathbb{R}^3\) has the origin \(o\) as an isolated umbilic point. It is proved, that the index \(l\) of \(o\) belongs to the set \(\{1,0, \dots, 1-k/2\}\) if \(k\) is even or \(\{1/2,-1/2, \dots, 1-k/2\}\) if \(k\) is odd. Conversely, for every number \(l\) of the above sets there exists a surface of the above type, so that \(l\) is the index of the isolated umbilic \(o\).
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1547911
zbMATH Keywords: homogeneous polynomial
zbMATH Keywords: graph
zbMATH Keywords: index
zbMATH Keywords: isolated umbilic
reviewed by: Friedrich Manhart
MaRDI profile type: Publication
full work available at URL: a:1005182230528
OpenAlex ID: W85739769
description: scientific article; zbMATH DE number 1547911