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Search: MSC category 53C60 ( Finsler spaces and generalizations (areal metrics) [See also 58B20] )

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1. CMB 2011 (vol 56 pp. 184)

Shen, Zhongmin
 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 quantityCategories:53C60, 53B40

2. CMB 2011 (vol 56 pp. 615)

Sevim, Esra Sengelen; Shen, Zhongmin
 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-curvatureCategories:53C60, 53B40

3. CMB 2011 (vol 55 pp. 474)

Chen, Bin; Zhao, Lili
 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 curvatureCategories:53B40, 53C60

4. CMB 2009 (vol 52 pp. 132)

Shen, Zhongmin
 On Projectively Flat $(\alpha,\beta)$-metrics The solutions to Hilbert's Fourth Problem in the regular case are projectively flat Finsler metrics. In this paper, we consider the so-called $(\alpha,\beta)$-metrics defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$, and find a necessary and sufficient condition for such metrics to be projectively flat in dimension $n \geq 3$. Categories:53B40, 53C60

5. CMB 2005 (vol 48 pp. 112)

Mo, Xiaohuan; Shen, Zhongmin
 On Negatively Curved Finsler Manifolds of Scalar Curvature In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension $n \geq 3$. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat Category:53C60