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...
Gauge complex field theory.
Gauge independent formulation of dynamics of charged extended objects
Gauge transformations on holomorphic bundles.
Generalized Miron's -connection in the recurrent -Hamilton spaces.
Geodesic reduction via frame bundle geometry.
Geometrical aspects of the covariant dynamics of higher order
We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra, [7]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations.
Geometrical background for the unified field theories : the Einstein-Cartan theory over a principal fibre bundle
Geometry of second-order connections and ordinary differential equations
The geometry of second-order systems of ordinary differential equations represented by -connections on the trivial bundle is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with...
Geometry on the space of positive functions.
Group actions, gauge transformations, and the calculus of variations.
Groups of Isometric Transformations, Basic Connections and Splitting results on Riemannian Manifolds
Hermitian-Einstein Connections and Stable Vector Bundles Over Compact Complex Surfaces.
Higher covariant derivatives.