4-Dimensional (Para)-Kähler-Weyl Structures
A characterization of the Riemann extension in terms of harmonicity
If is a manifold with a symmetric linear connection, then can be endowed with the natural Riemann extension (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure on and prove that is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if reduces to the...
A class of metrics on tangent bundles of pseudo-Riemannian manifolds
We provide the tangent bundle of pseudo-Riemannian manifold with the Sasaki metric and the neutral metric . First we show that the holonomy group of contains the one of . What allows us to show that if is indecomposable reducible, then the basis manifold is also indecomposable-reducible. We determine completely the holonomy group of according to the one of . Secondly we found conditions on the base manifold under which ( respectively ) is Kählerian, locally symmetric or Einstein...
A Kummer-type construction of self-dual 4-manifolds.
A local analytic splitting of the holonomy map on flat connections.
A locally symmetric Kähler Einstein structure on the cotangent bundle of a space form.
A locally symmetric Kähler Einstein structure on the tangent bundle of a space form.
A model of gauge theory with invariant variables.
A Narasimhan-Seshardri-Donaldson Correspondance over Non-orientable Surfaces.
A note on characteristic classes
This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.
A partial regularity result for a class of stationary Yang-Mills in high dimension.
We prove, for arbitrary dimension of the base n greater than or equal to 4, stationary Yang-Mills Fields satisfying Borne approximability property are regular apart from a closed subset of the base having zero (n-4)- Hausdorff measure.
A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
A rigidity property of class VIIo surface fundamental groups.
Abstract velocity functors
Affine analogues of the Sasaki-Shchepetilov connection
For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on...
An extension of a flat Koszul connection being a Maurer-Cartan form.
An introduction to gerbes on orbifolds
This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.
Asymptotic behavior of the L2-metric on moduli spaces of Yang-Mills connections.
Asymptotic behavior of the L2-metric on moduli spaces of Yang-Mills connections, II.
Asymptotic behaviour and the moduli space of doubly-periodic instantons
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus with a complex line , with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to . The converse statement is also true, namely a holomorphic bundle on which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton....