On affine motions with one-dimensional orbits in common spaces of paths
| Autor: | N. D. Nikitin, O. G. Nikitina |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Дифференциальная геометрия многообразий фигур, Vol 55, Iss 1, Pp 45-54 (2024) |
| Druh dokumentu: | article |
| ISSN: | 0321-4796 2782-3229 |
| DOI: | 10.5922/0321-4796-2024-55-1-5 |
| Popis: | The concept of a common path space was introduced by J. Duqlas. M. S. Knebelman was the first to consider affine and projective movements in these spaces. The general path space is a generalization of the space of affine connectivity. In this paper, we study spaces of paths that admit groups of affine motions with one-dimensional orbits. For each representation in the form of algebra of vector fields of the abelian Lie algebra and the Lr algebra containing the abelian ideal Lr-1, a system of equations of infinitesimal affine motions is compiled. The vector fields of each of these representations are operators of a group of transformations with one-dimensional orbits. Integrating this system, general spaces of paths are defined that admit a group of affine motions with one-dimensional orbits, the operators of which are the vector fields of these representations. The maximum order of these groups is set. It is shown that the spaces of paths admitting a group of affine motions with one-dimensional orbits of maximum order are projectively flat. The conditions that are necessary and sufficient for the space of paths to admit a group of affine motions with one-dimensional orbits of maximum order are given. |
| Databáze: | Directory of Open Access Journals |
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