1. CJM Online first
 Ciesielski, Krzysztof Chris; Jasinski, Jakub

Fixed point theorems for maps with local and pointwise contraction properties
The paper constitutes a comprehensive study of ten classes of
selfmaps on metric spaces $\langle X,d\rangle$ with the local
and pointwise (a.k.a. local radial) contraction properties.
Each of those classes appeared previously in the literature in
the context of fixed point theorems.
We begin with presenting an overview
of these fixed point results, including concise self contained
sketches of their proofs.
Then, we proceed with a discussion of the relations among the
ten classes of selfmaps with domains $\langle X,d\rangle$
having various topological properties which often appear in the
theory of fixed point theorems: completeness, compactness, (path)
connectedness, rectifiable path connectedness, and $d$convexity.
The bulk of the results presented in this part consists of examples
of maps that show nonreversibility of the previously established
inclusions between theses classes.
Among these examples, the most striking is a differentiable autohomeomorphism
$f$ of a compact perfect subset $X$ of $\mathbb R$
with $f'\equiv 0$, which constitutes also a minimal dynamical
system.
We finish with discussing a few remaining open problems on weather
the maps with specific pointwise contraction
properties must have the fixed points.
Keywords:fixed point, periodic point, contractive map, locally contractive map, pointwise contractive map, radially contractive map, rectifiably path connected space, dconvex, geodesic, remetrization contraction mapping principle Categories:54H25, 37C25 

2. CJM 2012 (vol 66 pp. 760)
 Hu, Shengda; Santoprete, Manuele

Regularization of the Kepler Problem on the Threesphere
In this paper we regularize the Kepler problem on $S^3$ in several
different ways. First, we perform a Mosertype regularization. Then, we
adapt the LigonSchaaf regularization to our problem. Finally, we show
that the Moser regularization and the LigonSchaaf map we obtained can be
understood as the composition of the corresponding maps for the Kepler problem
in Euclidean space and the gnomonic transformation.
Keywords:Kepler problem on the sphere, LigonShaaf regularization, geodesic flow on the sphere Category:70Fxx 

3. 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 

4. CJM 2004 (vol 56 pp. 776)
 Lim, Yongdo

Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices
We explicitly describe
the best approximation in
geodesic submanifolds of positive definite matrices
obtained from involutive
congruence transformations on the
CartanHadamard manifold ${\mathrm{Sym}}(n,{\Bbb R})^{++}$ of
positive definite matrices.
An explicit calculation for the minimal distance
function from the geodesic submanifold
${\mathrm{Sym}}(p,{\mathbb R})^{++}\times
{\mathrm{Sym}}(q,{\mathbb R})^{++}$ block diagonally embedded in
${\mathrm{Sym}}(n,{\mathbb R})^{++}$ is
given in terms of metric and
spectral geometric means, Cayley transform, and Schur
complements of positive definite matrices when $p\leq 2$ or $q\leq 2.$
Keywords:Matrix approximation, positive, definite matrix, geodesic submanifold, CartanHadamard manifold,, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transform Categories:15A48, 49R50, 15A18, 53C3 

5. 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 
