Connections in 2-fibered manifolds
Connections in associated fibre bundles
Connections in -vector bundles.
Connections in regular Poisson manifolds over ℝ-Lie foliations
The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally,...
Connections induced by -tensor fields on cotangent bundles
On cotangent bundles the Liouville field, the Liouville 1-form and the canonical symplectic structure d exist. In this paper interactions between these objects and -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.
Connections of higher order and product preserving functors
In this paper we consider a product preserving functor of order and a connection of order on a manifold . We introduce horizontal lifts of tensor fields and linear connections from to with respect to . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
Connections of order r
Connections on 1-jets principal fiber bundles
Connections on distributional bundles
Connections on embedded manifolds.
Connections on higher order principal prolongations
Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.
Connections on higher order tangent bundles
Connections on infinite dimensional manifolds with corners
Connections on -symplectic manifolds.
Connections on lie Algebroids and the Weil-Kostant Theorem
Connections on some functional bundles
Connections on the second tangent bundle
Connections partially adapted to a metric -structure
Connections with prescribed curvature
We discuss the problem of prescribing the curvature of a connection on a principal bundle whose base manifold is three-dimensional. In particular, we consider the local question: Given a curvature form , when does there exist locally a connection such that is the curvature of ? When the structure group of the bundle is semisimple, a finite number of nonlinear identities arise as necessary conditions for local solvability of the curvature equation. We conjecture that these conditions are also...
Connections with prescribed curvature and Yang-Mills currents : the semi-simple case