Surfaces which contain helical geodesics
type: Item
instance of: scholarly article
title: Surfaces which contain helical geodesics
zbMATH Open document ID: 0757.53003
DOI: 10.1007/BF02414069
author: Michiko Tamura
published in: Geometriae Dedicata
publication date: 1992-09-27T00:00:00Z
review text: Extending a result obtained jointly with \textit{N. Takeuchi} in Bull. Tokyo Gakugei Univ., Sect. IV., Math. Nat. Sci. 43, 5-8 (1991; Zbl 0755.53003) the author characterizes the type of a complete smooth surface of constant mean curvature \(M\) in \(E^ 3\) which contains many helical geodesics. The circular cylinder is characterized by the property that through each point there passes a non-straight helical geodesic under the additional condition that there are no umbilics on \(M\). The assumption of two helical geodesics through each points leads to a plane, a sphere or a circular cylinder.
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 58797
zbMATH Keywords: surface of constant mean curvature
zbMATH Keywords: helical geodesics
zbMATH Keywords: circular cylinder
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Q4064107
cites work: A surface which contains planar geodesics
cites work: Q3200157
description: scientific article; zbMATH DE number 58797