Geometry of G-Structures via the Intrinsic Torsion
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Geometry of G-Structures via the Intrinsic Torsion
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| Creator |
Niedziałomski, K.
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| 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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| Date |
2019-02-18T14:54:45Z
2019-02-18T14:54:45Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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