On connections with torsion on nonholonomic para-Kenmotsu manifolds
| Autor: | A. V. Bukusheva |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Дифференциальная геометрия многообразий фигур, Vol 54, Iss 1, Pp 49-63 (2023) |
| Druh dokumentu: | article |
| ISSN: | 0321-4796 2782-3229 |
| DOI: | 10.5922/0321-4796-2023-54-1-6 |
| Popis: | The concept of a nonholonomic para-Kenmotsu manifold is introduced. A nonholonomic para-Kenmotsu manifold is a natural generalization of a para-Kenmotsu manifold; the distribution of a nonholonomic para-Kenmotsu manifold does not need to be involutive. Properly nonholonomic para-Kenmotsu manifolds are singled out, these are nonholonomic para-Kenmotsu manifolds with non-involutive distribution. On an almost (para-)contact metric manifold, we introduce a metric connection with torsion, which is called a connection of Levi-Civita type in this paper. In the case of a nonholonomic para-Kenmotsu manifold, such a connection has a simpler structure than the Levi-Civita connection, and in some cases it turns out to be preferable from an applied point of view. A Levi-Civita type connection coincides with a Levi-Civita connection if and only if a nonholonomic para-Kenmotsu manifold reduces to a para-Kenmotsu manifold. It is proved that a proper nonholonomic para-Kenmotsu manifold cannot carry the structure of an Einstein manifold with respect to a connection of the Levi-Civita type. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|