Parallel transports in the connections of three types for cocongruence K(n-m)m
| Autor: | Belova O. O. |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Дифференциальная геометрия многообразий фигур, Vol 55, Iss 2, Pp 57-69 (2024) |
| Druh dokumentu: | article |
| ISSN: | 0321-4796 2782-3229 |
| DOI: | 10.5922/0321-4796-2024-55-2-4 |
| Popis: | We continue to study the cocongruence of -dimensional planes using the Cartan — Laptev method. In an -dimensional projective space , the cocongruence of -dimensional planes can be given by the following equations . Compositional clothing of a given cocongruence by fields of ()-planes : and points allows one to define connections of three types in the associated bundle. In the present paper, parallel transports of an analogue of Cartan plane are studied in the connections of three types. It is proved 4 theorems: 1. Parallel transport of the analogue of the Cartan plane in an arbitrary connection is freely degenerate, i. e., in general, there are no special transports of this clothing plane. 2. In the group connection of the first type, the parallel transport of an analog of the Cartan plane is connected degenerate, i. e., the plane will be fixed under parallel transport in this connection. 3. In the group connections of the second and third types, the parallel transport of the analogue of the Cartan plane is freely degenerate. 4. The analogue of the Cartan plane is transferred in parallel in a linear combination of the first type connection if and only if it is displaced in the plane . |
| Databáze: | Directory of Open Access Journals |
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