1. CMB Online first
|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
2. CMB 2011 (vol 55 pp. 474)
|A Note on Randers Metrics of Scalar Flag Curvature|
Some families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic $S$-curvature are given. Certain Randers metrics with Einstein $\alpha$ are considered and proved to be complex. Three dimensional Randers manifolds, with $\alpha$ having constant scalar curvature, are studied.
Keywords:Randers metrics, scalar flag curvature