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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148543 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometry of G-Structures via the Intrinsic Torsion / K. Niedziałomski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635375807168512 |
|---|---|
| author | Niedziałomski, K. |
| author_facet | Niedziałomski, K. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-30T17:43:32Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148543 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T17:43:32Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Niedziałomski, K. 2019-02-18T14:54:45Z 2019-02-18T14:54:45Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/148543 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometry of G-Structures via the Intrinsic Torsion Article published earlier |
| spellingShingle | Geometry of G-Structures via the Intrinsic Torsion Niedziałomski, K. |
| title | 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_short | Geometry of G-Structures via the Intrinsic Torsion |
| title_sort | geometry of g-structures via the intrinsic torsion |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148543 |
| work_keys_str_mv | AT niedziałomskik geometryofgstructuresviatheintrinsictorsion |