Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds
Let M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the...
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| Format: | Article |
| Language: | English |
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Immanuel Kant Baltic Federal University
2020-08-01
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| Series: | Дифференциальная геометрия многообразий фигур |
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| Online Access: | https://journals.kantiana.ru/geometry/4686/25776/ |
| _version_ | 1818295846727319552 |
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| author | A. Bukusheva |
| author_facet | A. Bukusheva |
| author_sort | A. Bukusheva |
| collection | DOAJ |
| description | Let M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the interior connection that allows parallel transport of admissible vectors along admissible curves. The assigment of the linear connection is equivalent to the assignment of a Riemannian metric of the Sasaki type on the distribution D. Certain tensor field of type (1,1) on D defines a so-called prolonged almost contact metric structure. Each section of the distribution D defines a morphism of smooth manifolds. It is proved that if a semi-invariant submanifold of the manifold M and is a covariantly constant vector field with respect to the N-connection , then is a semi-invariant submanifold of the manifold D with respect to the prolonged almost contact metric structure.
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| first_indexed | 2024-12-13T03:54:08Z |
| format | Article |
| id | doaj.art-0f2596b07b91437891d4c770196feb5b |
| institution | Directory Open Access Journal |
| issn | 0321-4796 2782-3229 |
| language | English |
| last_indexed | 2024-12-13T03:54:08Z |
| publishDate | 2020-08-01 |
| publisher | Immanuel Kant Baltic Federal University |
| record_format | Article |
| series | Дифференциальная геометрия многообразий фигур |
| spelling | doaj.art-0f2596b07b91437891d4c770196feb5b2022-12-22T00:00:38ZengImmanuel Kant Baltic Federal UniversityДифференциальная геометрия многообразий фигур0321-47962782-32292020-08-0151394810.5922/0321-4796-2020-51-5Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds A. Bukusheva0https://orcid.org/0000-0002-2930-1697Saratov State UniversityLet M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the interior connection that allows parallel transport of admissible vectors along admissible curves. The assigment of the linear connection is equivalent to the assignment of a Riemannian metric of the Sasaki type on the distribution D. Certain tensor field of type (1,1) on D defines a so-called prolonged almost contact metric structure. Each section of the distribution D defines a morphism of smooth manifolds. It is proved that if a semi-invariant submanifold of the manifold M and is a covariantly constant vector field with respect to the N-connection , then is a semi-invariant submanifold of the manifold D with respect to the prolonged almost contact metric structure. https://journals.kantiana.ru/geometry/4686/25776/almost contact metric manifoldsection of a distributionsemi-invariant manifoldprolonged almost contact metric structure |
| spellingShingle | A. Bukusheva Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds Дифференциальная геометрия многообразий фигур almost contact metric manifold section of a distribution semi-invariant manifold prolonged almost contact metric structure |
| title | Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds |
| title_full | Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds |
| title_fullStr | Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds |
| title_full_unstemmed | Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds |
| title_short | Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds |
| title_sort | lifting semi invariant submanifolds to distribution of almost contact metric manifolds |
| topic | almost contact metric manifold section of a distribution semi-invariant manifold prolonged almost contact metric structure |
| url | https://journals.kantiana.ru/geometry/4686/25776/ |
| work_keys_str_mv | AT abukusheva liftingsemiinvariantsubmanifoldstodistributionofalmostcontactmetricmanifolds |