Closed principal lines of surfaces immersed in the Euclidean 4-space
type: Item
instance of: scholarly article
title: Closed principal lines of surfaces immersed in the Euclidean 4-space
zbMATH Open document ID: 1050.53009
DOI: 10.1023/A:1015365309326
author: Yanyan Li
published in: Journal of Dynamical and Control Systems
publication date: 2002-12-15T00:00:00Z
review text: A closed principal curvature line on a surface \(M\) immersed in Euclidean 3-space is called a principal cycle. In the first part the authors give a definition of \(v\)-principal cycles in the case of a surface \(M\) immersed in Euclidean 4-space; hereby in \(p\in M\) it is \(v\in (T_pM)^\perp\). The main theorem gives an expression of the first derivative of Poincaré's map associated to a \(v\)-principal cycle by geometric invariants. The final part gives examples related to ruled surfaces and tubes.
reviewed by: Friedrich Manhart
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 1845274
zbMATH Keywords: principal curvature lines
zbMATH Keywords: principal cycles
MaRDI profile type: Publication
full work available at URL: a:1015365309326
OpenAlex ID: W111201403
description: scientific article; zbMATH DE number 1845274