On projective symmetries on Finsler Spaces
| Autor: | Lajmiri, Behnaz, Bidabad, Behroz, Rafie-Rad, Mehdi, Aryanejad-Keshavarzi, Yadollah |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Differential Geometry and its Applications 77(2021)101763 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.difgeo.2021.101763 |
| Popis: | 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. Comment: 25 pages |
| Databáze: | arXiv |
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