Weighted Projective Ricci Curvature in Finsler Geometry

2019/08/26 by T. Tabatabaeifar, Tabatabaeifar, T., Behzad Najafi +3 · 1 citation
Physics and Astronomy · Psychology · #53B40 #53C60 #Advanced Differential Geometry Research #Adventure Sports and Sensation Seeking #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1908.09465

openalex publication_date 2019/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

Citations

• On an Asymmetrical Metric in the Four-Space of General Relativity
• A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results

Cited by

• On the Generalized Projective Riemann Curvature in Finsler Geometry

Related

• On a Class of Weakly Weighted Einstein Metrics
• Classification of Randers metric of isotropic projective Ricci curvature
• On the Generalized Projective Riemann Curvature in Finsler Geometry
• On the projective Ricci curvature
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