Geometry of G-Structures via the Intrinsic Torsion
We study the geometry of a G-structure P inside the oriented orthonormal frame bundle SO(M) over an oriented Riemannian manifold M. We assume that G is connected and closed, so the quotient SO(n)/G, where n=dimM, is a normal homogeneous space and we equip SO(M) with the natural Riemannian structure...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148543 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Geometry of G-Structures via the Intrinsic Torsion / K. Niedziałomski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1485432019-02-19T01:24:15Z Geometry of G-Structures via the Intrinsic Torsion Niedziałomski, K. We study the geometry of a G-structure P inside the oriented orthonormal frame bundle SO(M) over an oriented Riemannian manifold M. We assume that G is connected and closed, so the quotient SO(n)/G, where n=dimM, is a normal homogeneous space and we equip SO(M) with the natural Riemannian structure induced from the structure on M and the Killing form of SO(n). We show, in particular, that minimality of P is equivalent to harmonicity of an induced section of the homogeneous bundle SO(M)×SO(n)SO(n)/G, with a Riemannian metric on M obtained as the pull-back with respect to this section of the Riemannian metric on the considered associated bundle, and to the minimality of the image of this section. We apply obtained results to the case of almost product structures, i.e., structures induced by plane fields. 2016 Article Geometry of G-Structures via the Intrinsic Torsion / K. Niedziałomski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C10; 53C24; 53C43; 53C15 DOI:10.3842/SIGMA.2016.107 http://dspace.nbuv.gov.ua/handle/123456789/148543 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study the geometry of a G-structure P inside the oriented orthonormal frame bundle SO(M) over an oriented Riemannian manifold M. We assume that G is connected and closed, so the quotient SO(n)/G, where n=dimM, is a normal homogeneous space and we equip SO(M) with the natural Riemannian structure induced from the structure on M and the Killing form of SO(n). We show, in particular, that minimality of P is equivalent to harmonicity of an induced section of the homogeneous bundle SO(M)×SO(n)SO(n)/G, with a Riemannian metric on M obtained as the pull-back with respect to this section of the Riemannian metric on the considered associated bundle, and to the minimality of the image of this section. We apply obtained results to the case of almost product structures, i.e., structures induced by plane fields. |
| format |
Article |
| author |
Niedziałomski, K. |
| spellingShingle |
Niedziałomski, K. Geometry of G-Structures via the Intrinsic Torsion Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Niedziałomski, K. |
| author_sort |
Niedziałomski, K. |
| title |
Geometry of G-Structures via the Intrinsic Torsion |
| title_short |
Geometry of G-Structures via the Intrinsic Torsion |
| title_full |
Geometry of G-Structures via the Intrinsic Torsion |
| title_fullStr |
Geometry of G-Structures via the Intrinsic Torsion |
| title_full_unstemmed |
Geometry of G-Structures via the Intrinsic Torsion |
| title_sort |
geometry of g-structures via the intrinsic torsion |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148543 |
| citation_txt |
Geometry of G-Structures via the Intrinsic Torsion / K. Niedziałomski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT niedziałomskik geometryofgstructuresviatheintrinsictorsion |
| first_indexed |
2023-05-20T17:29:43Z |
| last_indexed |
2023-05-20T17:29:43Z |
| _version_ |
1796153420028051456 |