The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the $ m $-th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish. Further, we prove that a locally conformally flat cubic Finsler metric with weakly isotropic scalar curvature must be locally Minkowskian.
Citation: Xiaoling Zhang, Cuiling Ma, Lili Zhao. On some $ m $-th root metrics[J]. AIMS Mathematics, 2024, 9(9): 23971-23978. doi: 10.3934/math.20241165
The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the $ m $-th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish. Further, we prove that a locally conformally flat cubic Finsler metric with weakly isotropic scalar curvature must be locally Minkowskian.
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Xiaoling Zhang, Cuiling Ma, Lili Zhao. On some $ m $-th root metrics[J]. AIMS Mathematics, 2024, 9(9): 23971-23978. doi: 10.3934/math.20241165
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