Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannia...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149011 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics / S.I. Vacaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862608504880103424 |
|---|---|
| author | Vacaru, S.I. |
| author_facet | Vacaru, S.I. |
| citation_txt | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics / S.I. Vacaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart-Moffat and Finsler-Lagrange spaces with connections compatible to a general nonsymmetric metric structure. Elaborating a metrization procedure for arbitrary distinguished connections, we define the class of distinguished linear connections which are compatible with the nonlinear connection and general nonsymmetric metric structures. The nonsymmetric gravity theory is formulated in terms of metric compatible connections. Finally, there are constructed such nonholonomic deformations of geometric structures when the Einstein and/or Lagrange-Finsler manifolds are transformed equivalently into spaces with generic local anisotropy induced by nonsymmetric metrics and generalized connections. We speculate on possible applications of such geometric methods in Einstein and generalized theories of gravity, analogous gravity and geometric mechanics.
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| first_indexed | 2025-11-28T17:34:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149011 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T17:34:52Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vacaru, S.I. 2019-02-19T12:56:53Z 2019-02-19T12:56:53Z 2008 Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics / S.I. Vacaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53A99; 53B40; 53C21; 53C12; 53C44; 53Z05; 83C20; 83D05; 83C99 https://nasplib.isofts.kiev.ua/handle/123456789/149011 We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart-Moffat and Finsler-Lagrange spaces with connections compatible to a general nonsymmetric metric structure. Elaborating a metrization procedure for arbitrary distinguished connections, we define the class of distinguished linear connections which are compatible with the nonlinear connection and general nonsymmetric metric structures. The nonsymmetric gravity theory is formulated in terms of metric compatible connections. Finally, there are constructed such nonholonomic deformations of geometric structures when the Einstein and/or Lagrange-Finsler manifolds are transformed equivalently into spaces with generic local anisotropy induced by nonsymmetric metrics and generalized connections. We speculate on possible applications of such geometric methods in Einstein and generalized theories of gravity, analogous gravity and geometric mechanics. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. The work is performed during a visit at Fields Institute. Author is grateful to Professors M. Anastasiei and J. Mof fat for kind support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics Article published earlier |
| spellingShingle | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics Vacaru, S.I. |
| title | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics |
| title_full | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics |
| title_fullStr | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics |
| title_full_unstemmed | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics |
| title_short | Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics |
| title_sort | einstein gravity, lagrange-finsler geometry, and nonsymmetric metrics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149011 |
| work_keys_str_mv | AT vacarusi einsteingravitylagrangefinslergeometryandnonsymmetricmetrics |