Fibrés de Higgs et connexions intégrables : le cas logarithmique (diviseur lisse)
Fibrés paraboliques stables et connexions singulières plates
Fibrés stables et métriques d'Hermite-Einstein
Fibrés vectoriels et principaux : notions de base
Flat manifolds with non-zero Euler characteristics.
Flow prolongation of some tangent valued forms
We study the prolongation of semibasic projectable tangent valued -forms on fibered manifolds with respect to a bundle functor on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear -th order connection on the base manifold, where is the base order of . We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent...
Foliate Partial Holomorphic Structures on Principal Bundles.
Forms equivalent to curvatures.
The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --> M and ξ' --> M are equivalent if there exist smooth fibered-linear mapsξ --> ξ' and W: ξ --> ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) > 2. Under favorable conditions the same holds at points where...