1. CMB 2015 (vol 58 pp. 530)
 Li, Benling; Shen, Zhongmin

Ricci Curvature Tensor and NonRiemannian 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 wellknown 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
nonRiemannian quantities. By this Ricci curvature tensor, we shall
have a better understanding on these nonRiemannian quantities.
Keywords:Finsler metrics, sprays, Ricci curvature, nonRiemanian quantity Categories:53B40, 53C60 

2. CMB 2014 (vol 57 pp. 765)
 da Silva, Rosângela Maria; Tenenblat, Keti

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type
We consider the Finsler space $(\bar{M}^3, \bar{F})$ obtained by
perturbing the Euclidean metric of $\mathbb{R}^3$ by a rotation. It
is the open region of $\mathbb{R}^3$ bounded by a cylinder with a
Randers metric. Using the BusemannHausdorff volume form, we
obtain the differential equation that characterizes the helicoidal
minimal surfaces in $\bar{M}^3$. We prove that the helicoid is a
minimal surface in $\bar{M}^3$, only if the axis of the helicoid
is the axis of the cylinder. Moreover, we prove that, in the
Randers space $(\bar{M}^3, \bar{F})$, the only minimal
surfaces in the Bonnet family, with fixed axis $O\bar{x}^3$, are the catenoids
and the helicoids.
Keywords:minimal surfaces, helicoidal surfaces, Finsler space, Randers space Categories:53A10, 53B40 

3. CMB 2012 (vol 57 pp. 209)
4. CMB 2012 (vol 57 pp. 194)
5. CMB 2011 (vol 56 pp. 184)
 Shen, Zhongmin

On Some NonRiemannian Quantities in Finsler Geometry
In this paper we study several nonRiemannian quantities in Finsler
geometry. These nonRiemannian quantities play an important role in
understanding the geometric properties of Finsler metrics. In
particular, we study a new nonRiemannian quantity defined by the
Scurvature. We show some relationships among the flag curvature,
the Scurvature, and the new nonRiemannian quantity.
Keywords:Finsler metric, Scurvature, nonRiemannian quantity Categories:53C60, 53B40 

6. 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, Scurvature Categories:53C60, 53B40 

7. 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 curvature Categories:53B40, 53C60 

8. CMB 2011 (vol 55 pp. 138)
9. 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 socalled $(\alpha,\beta)$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 

10. CMB 2002 (vol 45 pp. 232)
 Ji, Min; Shen, Zhongmin

On Strongly Convex Indicatrices in Minkowski Geometry
The geometry of indicatrices is the foundation of Minkowski geometry.
A strongly convex indicatrix in a vector space is a strongly convex
hypersurface. It admits a Riemannian metric and has a distinguished
invariant(Cartan) torsion. We prove the existence of nontrivial
strongly convex indicatrices with vanishing mean torsion and discuss
the relationship between the mean torsion and the Riemannian curvature
tensor for indicatrices of Randers type.
Categories:46B20, 53C21, 53A55, 52A20, 53B40, 53A35 
