Best pair of two skew lines over the octonions
type: Item
instance of: scholarly article
title: Best pair of two skew lines over the octonions
zbMATH Open document ID: 1325.51024
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Advances in Applied Clifford Algebras
publication date: 2015-09-23T00:00:00Z
full work available at URL: http://hdl.handle.net/10316/80262
review text: An octonion has a scalar part and a vector part. The pure octonions, i. e., all those with 0 as scalar part, can be isomorphically identified with \(\mathbb{R}^7\). Seven-dimensional space can then be endowed with a geometry, by defining points and lines in the usual manner, and defining line parallelism and orthogonality based on the dot and vector product of octonions. In this context, the authors determine the distance between two skew lines, i. e., the length of the shortest segment connecting them.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51N99
Mathematics Subject Classification ID: 17A35
zbMATH DE Number: 6484661
zbMATH Keywords: octonion equation of a line
zbMATH Keywords: orthogonal projection
zbMATH Keywords: inner product of octonions
zbMATH Keywords: parallel and perpendicular octonions
zbMATH Keywords: double vector cross product in \(\mathbb{R}^7\)
zbMATH Keywords: best approximation pair
Wikidata QID: Q57867175
MaRDI profile type: Publication
OpenAlex ID: W2060955051
cites work: Modern Kaluza-Klein theories
cites work: The hierarchy problem and new dimensions at a millimeter
cites work: The octonions
cites work: Vector cross products
cites work: Composition algebras and their automorphisms
cites work: Q5650526
cites work: The geometry of hypercomplex matrices
cites work: The triple cross product in \(\mathbb{R}^7\)
cites work: Q5566063
cites work: Warped radion dark matter
cites work: Q4856157
cites work: Large Mass Hierarchy from a Small Extra Dimension
cites work: Vector cross products inndimensions
cites work: Q4342008
DOI: 10.1007/S00006-015-0527-Z
description: scientific article; zbMATH DE number 6484661