Invariant characteristic of curves of quasi-quaternion space
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.53007
author: R. F. Dombrovs'kyj
author: N. F. Kyrnytska
publication date: 2002-01-06T00:00:00Z
Mathematics Subject Classification ID: 53A40
zbMATH DE Number: 1685506
zbMATH Keywords: invariant characteristic
zbMATH Keywords: curves of quasi-quaternion space
zbMATH Keywords: automorphism
MaRDI profile type: Publication
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title: Invariant characteristic of curves of quasi-quaternion space
published in: Kraĭovi Zadachi dlya Dyferentsial'nykh Rivnyan'
review text: The point real \(4n\)-dimensional affine space is called quasi-quaternion if on its lineal \(V_{4n}\) the automorphisms \(I\) and \(J\) are given by the properties \(I^2=-id\), \(J^2=-id\), \(IJ=JI\), where \(id\) is the identity automorphism, \(IJ\) is the composition of automorphisms. For continuously differentiable curves of a quasi-quaternion space the invariants are found, the partially canonical affine basis and the natural normalization are constructed. A classification theorem is proved and the differential geometry for some classes of curves in quasi-quaternion space is presented.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1685506