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Search: All articles in the CMB digital archive with keyword Finsler metric

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1. CMB Online first

Chen, Bin; Zhao, Lili
On a Yamabe type problem in Finsler geometry
In this paper, a new notion of scalar curvature for a Finsler metric $F$ is introduced, and two conformal invariants $Y(M,F)$ and $C(M,F)$ are defined. We prove that there exists a Finsler metric with constant scalar curvature in the conformal class of $F$ if the Cartan torsion of $F$ is sufficiently small and $Y(M,F)C(M,F)\lt Y(\mathbb{S}^n)$ where $Y(\mathbb{S}^n)$ is the Yamabe constant of the standard sphere.

Keywords:Finsler metric, scalar curvature, Yamabe problem
Categories:53C60, 58B20

2. CMB 2015 (vol 58 pp. 530)

Li, Benling; Shen, Zhongmin
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
Categories:53B40, 53C60

3. 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 quantity
Categories:53C60, 53B40

4. CMB 2011 (vol 55 pp. 138)

Li, Benling; Shen, Zhongmin
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

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