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arXiv · 2304.00496

On projective symmetries on Finsler Spaces

Behnaz Lajmiri·Behroz Bidabad·Mehdi Rafie-Rad·Yadollah Aryanejad-Keshavarzi
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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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Behnaz Lajmiri, Behroz Bidabad, Mehdi Rafie-Rad, Yadollah Aryanejad-Keshavarzi. 2023-04-02. On projective symmetries on Finsler Spaces. https://doi.org/10.1016/j.difgeo.2021.101763

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