1. CMB Online first
2. CMB Online first
 de Dios Pérez, Juan; Lee, Hyunjin; Suh, Young Jin; Woo, Changhwa

Real hypersurfaces in complex twoplane Grassmannians with Reeb parallel Ricci tensor in the GTW connection
There are several kinds of classification problems for real hypersurfaces
in complex twoplane Grassmannians $G_2({\mathbb C}^{m+2})$.
Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb
C}^{m+2})$ with Reeb parallel Ricci tensor in LeviCivita connection.
In this paper, we introduce the notion of generalized TanakaWebster
(in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface
$M$ in $G_2({\mathbb C}^{m+2})$. Next, we give a complete classification
of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with GTW Reeb
parallel Ricci tensor.
Keywords:Complex twoplane Grassmannian, real hypersurface, Hopf hypersurface, generalized TanakaWebster connection, parallelism, Reeb parallelism, Ricci tensor Categories:53C40, 53C15 

3. CMB 2015 (vol 58 pp. 835)
4. CMB 2014 (vol 58 pp. 158)
5. CMB 2011 (vol 55 pp. 611)
 Özgür, Cihan; Mihai, Adela

Chen Inequalities for Submanifolds of Real Space Forms with a SemiSymmetric NonMetric Connection
In this paper we prove Chen inequalities for submanifolds of real space
forms endowed with a semisymmetric nonmetric connection, i.e., relations
between the mean curvature associated with a semisymmetric nonmetric
connection, scalar and sectional curvatures, Ricci curvatures and the
sectional curvature of the ambient space. The equality cases are considered.
Keywords:real space form, semisymmetric nonmetric connection, Ricci curvature Categories:53C40, 53B05, 53B15 

6. CMB 2009 (vol 52 pp. 175)
 Biswas, Indranil

Connections on a Parabolic Principal Bundle, II
In \emph{Connections on a parabolic principal bundle over a curve, I}
we defined connections on a parabolic
principal bundle. While connections on usual principal bundles are
defined as splittings of the Atiyah exact sequence, it was noted in
the above article that the Atiyah exact sequence does not generalize to
the parabolic principal bundles.
Here we show that a twisted version
of the Atiyah exact sequence generalizes to the context of
parabolic principal bundles. For usual principal bundles, giving a
splitting of this twisted Atiyah exact sequence is equivalent
to giving a splitting of the Atiyah exact sequence. Connections on
a parabolic principal bundle can be defined using the
generalization of the twisted Atiyah exact sequence.
Keywords:Parabolic bundle, Atiyah exact sequence, connection Categories:32L05, 14F05 

7. CMB 2004 (vol 47 pp. 624)
 Zhang, Xi

A Compactness Theorem for YangMills Connections
In this paper, we consider YangMills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of YangMills
connections with the uniformly bounded $L^{\frac{m}{2}}$norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:YangMills connection, vector bundle, gauge transformation Categories:58E20, 53C21 

8. CMB 2001 (vol 44 pp. 129)
 CurrásBosch, Carlos

LinÃ©arisation symplectique en dimension 2
In this paper the germ of neighborhood of a compact leaf in a
Lagrangian foliation is symplectically classified when the compact
leaf is $\bT^2$, the affine structure induced by the Lagrangian
foliation on the leaf is complete, and the holonomy of $\bT^2$ in
the foliation linearizes. The germ of neighborhood is classified by a
function, depending on one transverse coordinate, this function is
related to the affine structure of the nearly compact leaves.
Keywords:symplectic manifold, Lagrangian foliation, affine connection Categories:53C12, 58F05 

9. CMB 1998 (vol 41 pp. 348)
 Tymchatyn, E. D.; Yang, ChangCheng

Characterizing continua by disconnection properties
We study Hausdorff continua in which every set of certain
cardinality contains a subset which disconnects the space. We show
that such continua are rimfinite. We give characterizations of
this class among metric continua. As an application of our
methods, we show that continua in which each countably infinite set
disconnects are generalized graphs. This extends a result of
Nadler for metric continua.
Keywords:disconnection properties, rimfinite continua, graphs Categories:54D05, 54F20, 54F50 
