On the Projective Algebra of Randers Metrics of Constant Flag Curvature
The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers spa...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147412 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the Projective Algebra of Randers Metrics of Constant Flag Curvature / M. Rafie-Rad, B. Rezaei // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719928692375552 |
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| author | Rafie-Rad, M. Rezaei, B. |
| author_facet | Rafie-Rad, M. Rezaei, B. |
| citation_txt | On the Projective Algebra of Randers Metrics of Constant Flag Curvature / M. Rafie-Rad, B. Rezaei // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2.
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| first_indexed | 2025-12-07T18:22:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147412 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:22:59Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rafie-Rad, M. Rezaei, B. 2019-02-14T17:58:53Z 2019-02-14T17:58:53Z 2011 On the Projective Algebra of Randers Metrics of Constant Flag Curvature / M. Rafie-Rad, B. Rezaei // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C60; 53B50, 58J60 DOI: http://dx.doi.org/10.3842/SIGMA.2011.085 https://nasplib.isofts.kiev.ua/handle/123456789/147412 The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2. The authors would like to express their grateful thanks to the referees for their valuable comments. This work was supported in part by the Institute for Research in Fundamental Sciences (IPM) by the grant No. 89530036. The first author wishes to thank Borzoo Nazari for many fruitful conversations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Projective Algebra of Randers Metrics of Constant Flag Curvature Article published earlier |
| spellingShingle | On the Projective Algebra of Randers Metrics of Constant Flag Curvature Rafie-Rad, M. Rezaei, B. |
| title | On the Projective Algebra of Randers Metrics of Constant Flag Curvature |
| title_full | On the Projective Algebra of Randers Metrics of Constant Flag Curvature |
| title_fullStr | On the Projective Algebra of Randers Metrics of Constant Flag Curvature |
| title_full_unstemmed | On the Projective Algebra of Randers Metrics of Constant Flag Curvature |
| title_short | On the Projective Algebra of Randers Metrics of Constant Flag Curvature |
| title_sort | on the projective algebra of randers metrics of constant flag curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147412 |
| work_keys_str_mv | AT rafieradm ontheprojectivealgebraofrandersmetricsofconstantflagcurvature AT rezaeib ontheprojectivealgebraofrandersmetricsofconstantflagcurvature |