1. CJM 2009 (vol 62 pp. 52)
 Deng, Shaoqiang

An Algebraic Approach to Weakly Symmetric Finsler Spaces
In this paper, we introduce a new algebraic notion, weakly symmetric
Lie algebras, to give an algebraic description of an
interesting class of homogeneous RiemannFinsler spaces, weakly symmetric
Finsler spaces. Using this new definition, we are able to give a
classification of weakly symmetric Finsler spaces with dimensions $2$
and $3$. Finally, we show that all the nonRiemannian reversible weakly
symmetric Finsler spaces we find are nonBerwaldian and with vanishing
Scurvature. This means that reversible nonBerwaldian Finsler spaces
with vanishing Scurvature may exist at large. Hence the generalized
volume comparison theorems due to Z. Shen are valid for a rather large
class of Finsler spaces.
Keywords:weakly symmetric Finsler spaces, weakly symmetric Lie algebras, Berwald spaces, Scurvature Categories:53C60, 58B20, 22E46, 22E60 

2. CJM 2009 (vol 61 pp. 1357)
 Shen, Zhongmin

On a Class of Landsberg Metrics in Finsler Geometry
In this paper, we study a long existing open problem on Landsberg
metrics in Finsler geometry. We consider Finsler metrics defined by a
Riemannian metric and a $1$form on a manifold. We show that a
\emph{regular} Finsler metric in this form is Landsbergian if and only if it
is Berwaldian. We further show that there is a twoparameter family of
functions, $\phi=\phi(s)$, for which there are a Riemannian metric
$\alpha$ and a $1$form $\beta$ on a manifold $M$ such that the scalar
function $F=\alpha \phi (\beta/\alpha)$ on $TM$ is an almost regular
Landsberg metric, but not a Berwald metric.
Categories:53B40, 53C60 

3. CJM 2003 (vol 55 pp. 112)
 Shen, Zhongmin

Finsler Metrics with ${\bf K}=0$ and ${\bf S}=0$
In the paper, we study the shortest time problem on a Riemannian space
with an external force. We show that such problem can be converted
to a shortest path problem on a Randers space. By choosing an
appropriate external force on the Euclidean space, we obtain a
nontrivial Randers metric of zero flag curvature. We also show that
any positively complete Randers metric with zero flag curvature must
be locally Minkowskian.
Categories:53C60, 53B40 
