On projective symmetries on Finsler spaces |
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Institution: | 1. Faculty of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., 15914 Tehran, Iran;2. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran;3. Department of Mathematics, Payame Noor University, 19395-4697 Tehran, Iran;4. Institut de Mathematique de Toulouse, Université Paul Sabatier, 118 route de NarbonneF-31062 Toulouse, France |
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Abstract: | There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of I-invariant projective vector fields. The sub-algebra of the C-projective vector fields, leaving the H-curvature invariant, has been studied extensively. Here we show on a closed Finsler space with negative definite Ricci curvature reduces to that of Killing vector fields. Moreover, if an Einstein-Finsler space admits such a projective vector field then the flag curvature is constant. Finally, a classification of compact isotropic mean Landsberg manifolds admitting certain projective vector fields is obtained with respect to the sign of Ricci curvature. |
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Keywords: | Projective vector Symmetries The physical meaning of projective Lie algebra Finsler Landsberg Isotropic mean Landsberg |
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