On projective symmetries on Finsler Spaces

DOI10.1016/J.DIFGEO.2021.101763arXiv2304.00496WikidataQ115354557 ScholiaQ115354557MaRDI QIDQ6431741

Y. Aryanejad-Keshavarzi, Behroz Bidabad, Author name not available (Why is that?), Mehdi Rafie-Rad

Publication date: 2 April 2023

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.

Mathematics Subject Classification ID

Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

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