1. CMB Online first
 Liu, Huaifu; Mo, Xiaohuan

Finsler warped product metrics of Douglas type
In this paper, we study the warped structures of Finsler metrics.
We obtain the differential equation that characterizes the Finsler
warped product metrics with vanishing Douglas curvature. By solving
this equation, we obtain all Finsler warped product Douglas metrics.
Some new Douglas Finsler metrics of this type are produced by
using known spherically symmetric Douglas metrics.
Keywords:Finsler metric, warped product, Douglas metric, spherically symmetric metric Categories:22E46, 53C30 

2. CMB 2011 (vol 55 pp. 870)
 Wang, Hui; Deng, Shaoqiang

Left Invariant EinsteinRanders Metrics on Compact Lie Groups
In this paper we study left invariant EinsteinRanders metrics on compact Lie
groups. First, we give a method to construct left invariant nonRiemannian EinsteinRanders metrics
on a compact Lie group, using the Zermelo navigation data.
Then we prove that this gives a complete classification of left invariant EinsteinRanders metrics on compact simple
Lie groups with the underlying Riemannian metric naturally reductive.
Further, we completely determine the identity component of the group of
isometries for this type of metrics on simple groups. Finally, we study some
geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature
of such metrics.
Keywords:EinsteinRanders metric, compact Lie groups, geodesic, flag curvature Categories:17B20, 22E46, 53C12 

3. CMB 2011 (vol 54 pp. 663)
 Haas, Ruth; G. Helminck, Aloysius

Admissible Sequences for Twisted Involutions in Weyl Groups
Let $W$ be a Weyl group, $\Sigma$ a set of simple reflections in $W$
related to a basis $\Delta$ for the root system $\Phi$ associated with
$W$ and $\theta$ an involution such that $\theta(\Delta) = \Delta$. We
show that the set of $\theta$twisted involutions in $W$,
$\mathcal{I}_{\theta} = \{w\in W \mid \theta(w) = w^{1}\}$ is in one
to one correspondence with the set of regular involutions
$\mathcal{I}_{\operatorname{Id}}$. The elements of $\mathcal{I}_{\theta}$ are
characterized by sequences in $\Sigma$ which induce an ordering called
the RichardsonSpringer Poset. In particular, for $\Phi$ irreducible,
the ascending RichardsonSpringer Poset of $\mathcal{I}_{\theta}$,
for nontrivial $\theta$ is identical to the descending
RichardsonSpringer Poset of $\mathcal{I}_{\operatorname{Id}}$.
Categories:20G15, 20G20, 22E15, 22E46, 43A85 
