Linear transformations of \(n\)-connections in \(\text{Osc}^2 M\). II (Q1432051)
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scientific article; zbMATH DE number 2074214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear transformations of \(n\)-connections in \(\text{Osc}^2 M\). II |
scientific article; zbMATH DE number 2074214 |
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Linear transformations of \(n\)-connections in \(\text{Osc}^2 M\). II (English)
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14 June 2004
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On the second order jet space \(J^2({\mathbb R},M)\) of a manifold \(M\), endowed with two Ehresmann connections, the authors consider the corresponding associated adapted bases in \(TE\) and \(T^*E\), and point out the relations between the holonomy coefficients of the adapted bases, between the torsion coefficients of a linear \(n\)-connection and between the coefficients of an arbitrary given metric \(n\)-tensor field on \(E\). For Part I, see Differ. Geom. Dyn. Syst. 2, No. 1, 18--31 (2000; Zbl 0977.53017).
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jet space
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osculator space
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adapted basis
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dual space
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connection
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torsion
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metric tensor
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