On the algebraic structure on the jet prolongations of fibred manifolds
On the Atiyah-Hitchin-Drinfeld-Manin Vanishing Theorem for Cohomology Groups of Instanton Bundles.
On the Chern-Weil homomorphism in Finsler spaces.
On the connections naturally induced on the second order frame bundle
On the Connections on the Prolongations of Principal Fibre Bundles
On the curvature of Chern-Lagrange connection.
On the existence of linear connection valued concomitants of geometric objects
On the existence of prolongations of connections by bundle functors.
On the exponential function of an ordered manifold with affine connection.
On the generalized Lagrange spaces associated to the remarkable Lagrangians.
On the geodesic projection of connections
On the Geometry of Associated Sheaves
On the geometry of vertical Weil bundles
We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections.
On the higher order geometry of Weil bundles over smooth manifolds and over parameter-dependent manifolds.
On the holonomity of higher order connections
On the iterated absolute differentiation on some functional bundles
We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.
On the kernel of holonomy.
A connection on a principal G-bundle may be identified with a smooth group morphism H : GL∞(M) → G, called a holonomy, where GL∞(M) is a group of equivalence classes of loops on the base M. The present article focuses on the kernel of this morphism, which consists of the classes of loops along which parallel transport is trivial. Use is made of a formula expressing the gauge potential as a suitable derivative of the holonomy, allowing a different proof of a theorem of Lewandowski’s, which states...
On the Kolář connection
Let be a fibred manifold with -dimensional base and -dimensional fibres and be a vector bundle with the same base and with -dimensional fibres (the same ). If and , we classify all canonical constructions of a classical linear connection on from a system consisting of a general connection on , a torsion free classical linear connection on , a vertical parallelism on and a linear connection on . An example of such is the connection by I. Kolář.
On the natural operators of Bianchi type
On the prolongation of vertical connections.