DOI: 10.3390/axioms12080784 ISSN:
Finsler Warped Product Metrics with Special Curvature Properties
Lingen Sun, Xiaoling Zhang, Mengke Wu- Geometry and Topology
- Logic
- Mathematical Physics
- Algebra and Number Theory
- Analysis
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing χ-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the χ-curvature vanishes if and only if the H-curvature vanishes.