1. 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
2. CMB 2011 (vol 56 pp. 615)
|Randers Metrics of Constant Scalar Curvature|
Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic.
Keywords:Randers metrics, scalar curvature, S-curvature