@article{Li2025, 
author = {Yanlin Li and Yuquan Xie and Manish Kumar Gupta and Suman Sharma},
title = {On projective Ricci curvature of cubic metrics},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {11305-11315},
keywords = {Finsler space, cubic metrics, S-curvature, Riemann curvature, Ricci curvature, projective Ricci curvature},
url = {https://www.sciopen.com/article/10.3934/math.2025513},
doi = {10.3934/math.2025513},
abstract = {To study the projective Ricci curvature (PRic-curvature) in Finsler geometry is interesting because it reflects the geometric properties that are invariant under the projective transformation. In this paper, we firstly derived an expression of S-curvature for the cubic Finsler metric and proved that this S-curvature vanishes if and only if    β is a constant Killing form. Next, we obtain an explicit expression of projective Ricci curvature for the cubic metric. We also proved that for the projective Ricci-flat Finsler space, the    1-form    β is closed, and then the Riemannian metric of    α is also Ricci-flat. Finally, we show that the cubic Finsler metric is of weak projective Ricci curvature if and only if it is projectively Ricci-flat.}
}