The Chen-type of the spiral surfaces
type: Item
instance of: scholarly article
title: The Chen-type of the spiral surfaces
zbMATH Open document ID: 0836.53001
DOI: 10.1007/BF03322254
author: Christos Baikoussis
author: Leopold Verstraelen
published in: Results in Mathematics
publication date: 1995-01-01T00:00:00Z
review text: A spiral surface is generated by rotating a plane curve \(C\) about an axis \(A\) contained in the plane of the curve \(C\) and simultaneously transforming \(C\) homothetically relative to a point of \(A\). In this paper, the authors study the type number and the Gauss map of spiral surfaces and prove the following results: Theorem 1. A spiral surface \(M\) in Euclidean 3-space \(E^3\) is of finite type if and only if \(M\) is minimal. Theorem 2. The plane is the only spiral surface in \(E^3\) with finite type Gauss map. Theorem 3. The plane is the only spiral surface in \(E^3\) whose Gauss map \(G\) satisfies \(\Delta G = \Lambda G\), where \(\Lambda\) is an endomorphism of \(E^3\).
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 828273
zbMATH Keywords: Chen type
zbMATH Keywords: finite type surface
zbMATH Keywords: spiral surface
zbMATH Keywords: Gauss map
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322254
OpenAlex ID: W2094814964
description: scientific article; zbMATH DE number 828273