On the scalar components of the canonical form on higher order frame bundles
| Autor: | A. V. Kuleshov |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Дифференциальная геометрия многообразий фигур, Vol 55, Iss 1, Pp 34-44 (2024) |
| Druh dokumentu: | article |
| ISSN: | 0321-4796 2782-3229 |
| DOI: | 10.5922/0321-4796-2024-55-1-4 |
| Popis: | A detailed obtaining of the expressions for the scalar components of the canonical form on higher order frame bundles over a smooth manifold has been done. The canonical form on the frame bundle of order p + 1 over an n-dimensional smooth manifold is a vector-valued differential 1-form with values in the tangent space to the p-th order frame bundle over the n-dimensional arithmetical space at the unit of the p-th order differential group. The scalar components of the canonical form are its coefficients with respect to natural basis of the tangent space. For every frame, there exists a polynomial mapping representing the frame in a given local chart on the manifold. Therefore, for any tangent vector to the frame bundle there is a first order Taylor expansion of one-parametric family of polynomial mappings representing the tangent vector. We obtain the formulas of the scalar components from the equations for coefficients of the two expansions for some tangent vector. |
| Databáze: | Directory of Open Access Journals |
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