1. CJM 2012 (vol 65 pp. 66)
 Deng, Shaoqiang; Hu, Zhiguang

On Flag Curvature of Homogeneous Randers Spaces
In this paper we give an explicit formula for the flag curvature of
homogeneous Randers spaces of Douglas type and apply this formula to
obtain some interesting results. We first deduce an explicit formula
for the flag curvature of an arbitrary left invariant Randers metric
on a twostep nilpotent Lie group. Then we obtain a classification of
negatively curved homogeneous Randers spaces of Douglas type. This
results, in particular, in many examples of homogeneous nonRiemannian
Finsler spaces with negative flag curvature. Finally, we prove a
rigidity result that a homogeneous Randers space of Berwald type whose
flag curvature is everywhere nonzero must be Riemannian.
Keywords:homogeneous Randers manifolds, flag curvature, Douglas spaces, twostep nilpotent Lie groups Categories:22E46, 53C30 

2. CJM 2009 (vol 61 pp. 1201)
 Arvanitoyeorgos, Andreas; Dzhepko, V. V.; Nikonorov, Yu. G.

Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
A Riemannian manifold $(M,\rho)$ is called Einstein if the metric
$\rho$ satisfies the condition \linebreak$\Ric (\rho)=c\cdot \rho$ for some
constant $c$. This paper is devoted to the investigation of
$G$invariant Einstein metrics, with additional symmetries,
on some homogeneous spaces $G/H$ of classical groups.
As a consequence, we obtain new invariant Einstein metrics on some
Stiefel manifolds $\SO(n)/\SO(l)$.
Furthermore, we show that for any positive integer $p$ there exists a
Stiefel manifold $\SO(n)/\SO(l)$
that admits at least $p$
$\SO(n)$invariant Einstein metrics.
Keywords:Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifolds Categories:53C25, 53C30 

3. CJM 2006 (vol 58 pp. 282)
 Fels, M. E.; Renner, A. G.

Nonreductive Homogeneous PseudoRiemannian Manifolds of Dimension Four
A method, due to \'Elie Cartan, is used to give an algebraic
classification of the nonreductive homogeneous pseudoRiemannian
manifolds of dimension four. Only one case with Lorentz signature can
be Einstein without having constant curvature, and two cases with
$(2,2)$ signature are Einstein of which one is Ricciflat. If a
fourdimensional nonreductive homogeneous pseudoRiemannian manifold
is simply connected, then it is shown to be diffeomorphic to
$\reals^4$. All metrics for the simply connected nonreductive
Einstein spaces are given explicitly. There are no nonreductive
pseudoRiemannian homogeneous spaces of dimension two and none of
dimension three with connected isotropy subgroup.
Keywords:Homogeneous pseudoRiemannian, Einstein space Category:53C30 

4. CJM 1998 (vol 50 pp. 1298)
 Milson, Robert

Imprimitively generated Liealgebraic Hamiltonians and separation of variables
Turbiner's conjecture posits that a Liealgebraic Hamiltonian
operator whose domain is a subset of the Euclidean plane admits a
separation of variables. A proof of this conjecture is given in
those cases where the generating Liealgebra acts imprimitively.
The general form of the conjecture is false. A counterexample is
given based on the trigonometric OlshanetskyPerelomov potential
corresponding to the $A_2$ root system.
Categories:35Q40, 53C30, 81R05 

5. CJM 1997 (vol 49 pp. 1323)
 Sankaran, Parameswaran; Zvengrowski, Peter

Stable parallelizability of partially oriented flag manifolds II
In the first paper with the same title the authors
were able to determine all partially oriented flag
manifolds that are stably parallelizable or
parallelizable, apart from four infinite families
that were undecided. Here, using more delicate
techniques (mainly Ktheory), we settle these
previously undecided families and show that none of
the manifolds in them is stably parallelizable,
apart from one 30dimensional manifold which still
remains undecided.
Categories:57R25, 55N15, 53C30 
