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: A. Bejancu, H. R. Farran
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171200002179
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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.
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1687-0425
language English
publishDate 2000-01-01
publisher Wiley
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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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AT abejancu geometriccharacterizationoffinslermanifoldsofconstantcurvaturek1
AT hrfarran geometriccharacterizationoffinslermanifoldsofconstantcurvaturek1