1. CMB Online first
2. CMB Online first
 Casini, Emanuele; Miglierina, Enrico; Piasecki, Lukasz

Hyperplanes in the space of convergent sequences and preduals of $\ell_1$
The main aim of the present paper is to investigate various structural
properties
of hyperplanes of $c$, the Banach space of the convergent sequences.
In particular, we give an explicit formula for the projection
constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$complemented. Moreover,
we obtain the classification
of those hyperplanes for which their duals are isometric to
$\ell_{1}$ and we give a complete description of the preduals
of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$
is weak$^{*}$convergent.
Keywords:space of convergent sequences, projection, $\ell_1$predual, hyperplane Categories:46B45, 46B04 

3. CMB 2014 (vol 57 pp. 697)
4. CMB 2013 (vol 57 pp. 72)
 Grari, A.

Un Anneau Commutatif associÃ© Ã un design symÃ©trique
Dans les articles \cite{1}, \cite{2} et \cite{3}; l'auteur dÃ©veloppe une reprÃ©sentation
d'un plan projectif fini par un
anneau commutatif unitaire dont les propriÃ©tÃ©s algÃ©briques dÃ©pendent
de la structure gÃ©omÃ©trique du plan. Dans l'article \cite{4}; il Ã©tend cette reprÃ©sentation aux designs symÃ©triques. Cependant l'auteur de l'article \cite{7} fait remarquer que la multiplication dÃ©finie dans ce cas ne peut Ãªtre associative que si le design est un plan projectif.
Dans ce papier on mÃ¨nera
une Ã©tude de cette reprÃ©sentation dans le cas des designs
symÃ©triques. On y montrera comment on peut faire associer un
anneau commutatif unitaire Ã
tout design symÃ©trique , on y prÃ©cisera certaines de ses propriÃ©tÃ©s, en
particulier, celles qui relÃ¨vent de son invariance. On caractÃ©risera aussi les gÃ©omÃ©tries projectives finies de dimension supÃ©rieure moyennant cette reprÃ©sentation.
Keywords:projective planes, symmetric designs, commutative rings Categories:05B05, 16S99 

5. CMB 2013 (vol 57 pp. 821)
 Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin

Real Hypersurfaces in Complex TwoPlane Grassmannians with Reeb Parallel Structure Jacobi Operator
In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex twoplane Grassmannians ${ { {G_2({\mathbb
C}^{m+2})} } }$, which means a
tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in
${G_2({\mathbb C}^{m+2})}$, by
the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords:real hypersurfaces, complex twoplane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 

6. CMB 2011 (vol 56 pp. 593)
7. CMB 2011 (vol 55 pp. 767)
 Martini, Horst; Wu, Senlin

On Zindler Curves in Normed Planes
We extend the notion of Zindler curve from the Euclidean plane to
normed planes. A characterization of Zindler curves for general
normed planes is given, and the relation between Zindler curves and
curves of constant areahalving distances in such planes is
discussed.
Keywords:rc length, areahalving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve Categories:52A21, 52A10, 46C15 

8. CMB 2010 (vol 53 pp. 629)
9. CMB 2009 (vol 52 pp. 424)
 Martini, Horst; Spirova, Margarita

Covering Discs in Minkowski Planes
We investigate the following version of the circle covering
problem in strictly convex (normed or) Minkowski planes: to cover
a circle of largest possible diameter by $k$ unit circles. In
particular, we study the cases $k=3$, $k=4$, and $k=7$. For $k=3$
and $k=4$, the diameters under consideration are described in
terms of sidelengths and circumradii of certain inscribed regular
triangles or quadrangles. This yields also simple explanations of
geometric meanings that the corresponding homothety ratios have.
It turns out that basic notions from Minkowski geometry play an
essential role in our proofs, namely Minkowskian bisectors,
$d$segments, and the monotonicity lemma.
Keywords:affine regular polygon, bisector, circle covering problem, circumradius, $d$segment, Minkowski plane, (strictly convex) normed plane Categories:46B20, 52A21, 52C15 

10. CMB 2005 (vol 48 pp. 523)
 Düvelmeyer, Nico

Angle Measures and Bisectors in Minkowski Planes
\begin{abstract}
We prove that a Minkowski plane is Euclidean if and only if Busemann's or
Glogovskij's definitions
of angular bisectors coincide
with a bisector defined by an angular measure in the sense of Brass.
In addition, bisectors defined by the area measure coincide with bisectors
defined by the circumference (arc length) measure
if and only if the unit circle is an
equiframed curve.
Keywords:Radon curves, Minkowski geometry, Minkowski planes,, angular bisector, angular measure, equiframed curves Categories:52A10, 52A21 
