1. CJM 2009 (vol 61 pp. 721)
 Calin, Ovidiu; Chang, DerChen; Markina, Irina

SubRiemannian Geometry on the Sphere $\mathbb{S}^3$
We discuss the subRiemannian
geometry induced by two noncommutative
vector fields which are left invariant
on the Lie group $\mathbb{S}^3$.
Keywords:noncommutative Lie group, quaternion group, subRiemannian geodesic, horizontal distribution, connectivity theorem, holonomic constraint Categories:53C17, 53C22, 35H20 

2. CJM 2004 (vol 56 pp. 566)
 Ni, Yilong

Geodesics in a Manifold with Heisenberg Group as Boundary
The Heisenberg group is considered as the boundary of a manifold. A class
of hypersurfaces in this manifold can be regarded as copies of the Heisenberg
group. The properties of geodesics in the interior and on the hypersurfaces
are worked out in detail. These properties are strongly related to those of
the Heisenberg group.
Keywords:Heisenberg group, Hamiltonian mechanics, geodesic Categories:53C22, 53C17 

3. CJM 2003 (vol 55 pp. 1080)
 Kellerhals, Ruth

Quaternions and Some Global Properties of Hyperbolic $5$Manifolds
We provide an explicit thick and thin decomposition for oriented
hyperbolic manifolds $M$ of dimension $5$. The result implies improved
universal lower bounds for the volume $\rmvol_5(M)$ and, for $M$
compact, new estimates relating the injectivity radius and the diameter
of $M$ with $\rmvol_5(M)$. The quantification of the thin part is
based upon the identification of the isometry group of the universal
space by the matrix group $\PS_\Delta {\rm L} (2,\mathbb{H})$ of
quaternionic $2\times 2$matrices with Dieudonn\'e determinant
$\Delta$ equal to $1$ and isolation properties of $\PS_\Delta {\rm
L} (2,\mathbb{H})$.
Categories:53C22, 53C25, 57N16, 57S30, 51N30, 20G20, 22E40 
