Главная
» Электронная библиотека » Contact and almost contact structures on the real extension of the Lobachevsky plane
Contact and almost contact structures on the real extension of the Lobachevsky plane
| Категория: | физико-математические науки | |
| Авторы (ПГУ): | Паньженский Владимир Иванович [100]  , Растрепина Анастасия Олеговна [0] | |
| Аннотация: | In this article, we propose a group model G of a real extension of the Lobachevsky plane H2 x R. The group G is a Lie group of special-form matrices and a subgroup of the general linear group GL(3, R). It is proved that, on the group model of the real extension of the Lobachevsky plane, there is a unique left-invariant almost contact metric structure with the Riemannian metric of the direct product that is invariant with respect to the isometry group. The concept of a linear connection compatible with the distribution is introduced. All left-invariant linear connections for which the tensors of the almost contact metric structure (eta, xi, phi, g) are covariantly constant are found. Among the left-invariant differential 1-forms, a canonical form defining a contact structure on G is distinguished. The left-invariant contact metric connections are found. There is a unique left-invariant connection for which all tensors of the almost contact metric structure and the canonical contact form are covariantly constant. It is proved that this connection is compatible with the contact distribution in the sense that a single geodesic tangent to the contact distribution passes through each point in each contact direction. Parametric equations of geodesics of the given connection are found. It is also established that the Levi-Civita connection of the Riemannian metric of the direct product is not a connection compatible with the contact distribution. | |
| Тип: | Статья | |
| Вид: | электронная копия бумажного издания | |
| Количество частей: | 1 | |
| Год издания: | 2021 | |
| Издательство: | Федеральное государственное автономное образовательное учреждение высшего образования "Казанский (Приволжский) федеральный университет" | |
| Где опубликовано: | Журнал | |
| Индексация: | Web of Science Core Collection, входящем в 3 (Q3) и 4 (Q4) квартили (тип документа Article, Review, Proceedings Paper, Book Chapter) | |
| Целевая аудитория: | Исследователь | |
| Целевое назначение: | Научное | |
| Лицензия: | Нет ограничений | |
| Ограничения: | Нет ограничений | |
| Правообладатель: | ФГАОУ ВО "Казанский (Приволжский) федеральный университет", Паньженский В.И., Растрепина А.О. | |
| ISSN: | 2541-7746 | |
| УДК: | 514.763 | |
| DOI: | 10.26907/2541-7746.2021.3-4.291-303 | |
| Библиографическая ссылка: | Pan’zhenskii V.I., Rastrepina A.O. Contact and almost contact structures on the real extension of the Lobachevsky plane. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2021, vol. 163, no. 3–4, pp. 291–303. doi: 10.26907/2541-7746.2021.3-4.291-303. (In Russian) | |
| Страницы (с ... по ...): | с 291 по 303 | |
| Том: | 163 (3-4) | |
| Внешняя веб-ссылка: | https://www.webofscience.com/wos/woscc/full-record/WOS:000782228000005 | |
| Язык: | Русский | |
| Место хранения: | Вне ПГУ | |
| Дата размещения: | 17.09.2022 | |
| Владелец: | Паньженский Владимир Иванович | |
| Ссылка на ресурс: | http://elib.pnzgu.ru/library/1663446303  | |
| Формат: | Не указан |