The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space
type: Item
instance of: scholarly article
title: The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space
zbMATH Open document ID: 0978.53004
author: Takashi Sano
author: Donghe Pei
published in: Tokyo Journal of Mathematics
publication date: 2002-01-23T00:00:00Z
review text: The paper deals with the intrinsic geometry of curves in a pseudo Euclidean 3-space (``Minkowski 3-space'', ``pe-space''). Analyzing the instantaneous kinematics of the moving trihedral the authors calculate expressions for the osculating pe-circle, the (hyper)-osculating pe-sphere and the generator of the axoidal surface belonging to a not lightlike (i.e., not isotropic) curve \(c\). The paper is not based on ``classical'' related references [e.g., \textit{O. Giering}, ``Vorlesungen über höhere Geometrie'' (1982; Zbl 0493.51001)]. So besides some typos there occur some less usual terms as for example ``focal developable'' for the surface enveloped by the pe-normal planes of curve \(c\), ``binormal indicatrix'' for the pe-spherical image of the binormals of \(c\), ``hyperbola and concentric pseudo sphere'' for a pair of conjugate pe-spheres.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 1523378
zbMATH Keywords: Minkowski space
zbMATH Keywords: curve theory
zbMATH Keywords: instantaneous kinematics
reviewed by: Gunter Weiss
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1255958816
OpenAlex ID: W2069540047
DOI: 10.3836/TJM/1255958816
description: scientific article; zbMATH DE number 1523378