Invariant characteristic of curves of quasi-quaternion space
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.
scientific article; zbMATH DE number 1685506