Invariant characteristic of curves of quasi-quaternion space (Q2761515)
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scientific article; zbMATH DE number 1685506
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant characteristic of curves of quasi-quaternion space |
scientific article; zbMATH DE number 1685506 |
Statements
6 January 2002
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invariant characteristic
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curves of quasi-quaternion space
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automorphism
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0.9036608
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0.8936103
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0.88999134
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0.88701886
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0.8846394
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Invariant characteristic of curves of quasi-quaternion space (English)
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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.
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