1. CMB Online first
|Ricci Curvature Tensor and Non-Riemannian Quantities|
There are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. By this Ricci curvature tensor, we shall have a better understanding on these non-Riemannian quantities.
Keywords:Finsler metrics, sprays, Ricci curvature, non-Riemanian quantity
2. CMB 2011 (vol 56 pp. 184)
|On Some Non-Riemannian Quantities in Finsler Geometry|
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 study a new non-Riemannian quantity defined by the S-curvature. We show some relationships among the flag curvature, the S-curvature, and the new non-Riemannian quantity.
Keywords:Finsler metric, S-curvature, non-Riemannian quantity
3. CMB 2011 (vol 55 pp. 138)
|Projectively Flat Fourth Root Finsler Metrics|
In this paper, we study locally projectively flat fourth root Finsler metrics and their generalized metrics. We prove that if they are irreducible, then they must be locally Minkowskian.
Keywords:projectively flat, Finsler metric, fourth root Finsler metric