Generalized Affine Connections Associated with the Space of Centered Planes
Our purpose is to study a space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> of centered <i>m</i>-planes in <i>n</i&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/7/782 |
| _version_ | 1797538718165237760 |
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| author | Olga Belova |
| author_facet | Olga Belova |
| author_sort | Olga Belova |
| collection | DOAJ |
| description | Our purpose is to study a space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> of centered <i>m</i>-planes in <i>n</i>-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered. |
| first_indexed | 2024-03-10T12:35:22Z |
| format | Article |
| id | doaj.art-0654f79d3819429bbbe163f6c8b854e4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:35:22Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0654f79d3819429bbbe163f6c8b854e42023-11-21T14:18:07ZengMDPI AGMathematics2227-73902021-04-019778210.3390/math9070782Generalized Affine Connections Associated with the Space of Centered PlanesOlga Belova0Institute of Physical and Mathematical Sciences and IT, Immanuel Kant Baltic Federal University, A. Nevsky Str. 14, 236016 Kaliningrad, RussiaOur purpose is to study a space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> of centered <i>m</i>-planes in <i>n</i>-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered.https://www.mdpi.com/2227-7390/9/7/782projective spacespace of centered planesplanar generalized affine connectionnormal generalized affine connection |
| spellingShingle | Olga Belova Generalized Affine Connections Associated with the Space of Centered Planes Mathematics projective space space of centered planes planar generalized affine connection normal generalized affine connection |
| title | Generalized Affine Connections Associated with the Space of Centered Planes |
| title_full | Generalized Affine Connections Associated with the Space of Centered Planes |
| title_fullStr | Generalized Affine Connections Associated with the Space of Centered Planes |
| title_full_unstemmed | Generalized Affine Connections Associated with the Space of Centered Planes |
| title_short | Generalized Affine Connections Associated with the Space of Centered Planes |
| title_sort | generalized affine connections associated with the space of centered planes |
| topic | projective space space of centered planes planar generalized affine connection normal generalized affine connection |
| url | https://www.mdpi.com/2227-7390/9/7/782 |
| work_keys_str_mv | AT olgabelova generalizedaffineconnectionsassociatedwiththespaceofcenteredplanes |