A Geometric characterization of Finsler manifolds of constant curvature K=1
We prove that a Finsler manifold 𝔽m is of constant curvature K=1 if and only if the unit horizontal Liouville vector field is a Killing vector field on the indicatrix bundle IM of 𝔽m.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200002179 |
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| _version_ | 1849692105573662720 |
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| author | A. Bejancu H. R. Farran |
| author_facet | A. Bejancu H. R. Farran |
| author_sort | A. Bejancu |
| collection | DOAJ |
| description | We prove that a Finsler manifold 𝔽m is of constant
curvature K=1 if and only if the unit horizontal Liouville vector
field is a Killing vector field on the indicatrix bundle IM of
𝔽m. |
| format | Article |
| id | doaj-art-b0de2e8ff592424bb525310c5e8d28d4 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b0de2e8ff592424bb525310c5e8d28d42025-08-20T03:20:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0123639940710.1155/S0161171200002179A Geometric characterization of Finsler manifolds of constant curvature K=1A. Bejancu0H. R. Farran1Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, KuwaitDepartment of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, KuwaitWe prove that a Finsler manifold 𝔽m is of constant curvature K=1 if and only if the unit horizontal Liouville vector field is a Killing vector field on the indicatrix bundle IM of 𝔽m.http://dx.doi.org/10.1155/S0161171200002179Finsler manifold of constant curvatureKilling vector fieldindicatrix bundlehorizontal Liouville vector field. |
| spellingShingle | A. Bejancu H. R. Farran A Geometric characterization of Finsler manifolds of constant curvature K=1 International Journal of Mathematics and Mathematical Sciences Finsler manifold of constant curvature Killing vector field indicatrix bundle horizontal Liouville vector field. |
| title | A Geometric characterization of Finsler manifolds of constant
curvature K=1 |
| title_full | A Geometric characterization of Finsler manifolds of constant
curvature K=1 |
| title_fullStr | A Geometric characterization of Finsler manifolds of constant
curvature K=1 |
| title_full_unstemmed | A Geometric characterization of Finsler manifolds of constant
curvature K=1 |
| title_short | A Geometric characterization of Finsler manifolds of constant
curvature K=1 |
| title_sort | geometric characterization of finsler manifolds of constant curvature k 1 |
| topic | Finsler manifold of constant curvature Killing vector field indicatrix bundle horizontal Liouville vector field. |
| url | http://dx.doi.org/10.1155/S0161171200002179 |
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