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1. CMB 2011 (vol 55 pp. 611)
Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space
forms endowed with a semi-symmetric non-metric connection, i.e., relations
between the mean curvature associated with a semi-symmetric non-metric
connection, scalar and sectional curvatures, Ricci curvatures and the
sectional curvature of the ambient space. The equality cases are considered.
Keywords:real space form, semi-symmetric non-metric connection, Ricci curvature Categories:53C40, 53B05, 53B15 |
2. CMB 2009 (vol 52 pp. 175)
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 |
3. CMB 2004 (vol 47 pp. 624)
A Compactness Theorem for Yang-Mills Connections In this paper, we consider Yang-Mills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of Yang-Mills
connections with the uniformly bounded $L^{\frac{m}{2}}$-norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:Yang-Mills connection, vector bundle, gauge transformation Categories:58E20, 53C21 |
4. CMB 2001 (vol 44 pp. 129)
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 |
5. CMB 1998 (vol 41 pp. 348)
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 rim-finite. 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, rim-finite continua, graphs Categories:54D05, 54F20, 54F50 |