On the Prolongations of Differentiable Distributions
On the reducibility of connections on the prolongations of vector bundles
On The Relation Between Connection And Sprays.
On the space of maps inducing isomorphic connections
Let be the universal connection on the bundle . Given a principal -bundle with connection , we determine the homotopy type of the space of maps of into such that is isomorphic to . Here denotes pull-back.
On the stratification of the orbit space for the action of automorphisms on connections [Book]
On the structure equations of the induced linear connections.
On the torsion of linear higher order connections
For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.
On the torsion of spaces with connection
On third order semiholonomic prolongation of a connection
We recall several different definitions of semiholonomic jet prolongations of a fibered manifold and use them to derive some interesting properties of prolongation of a first order connection to a third order semiholonomic connection.
On torsion of a -web
A 3-web on a smooth -dimensional manifold can be regarded locally as a triple of integrable -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a -web and its properties by invariant -tensor fields and where is a projector and id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor of the Chern connection through...
On transformation groups of -linear connections in the bundle of accelerations.
On -recurrent generalized -contact metric manifolds.
Only one of generalized gradients can be elliptic
Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
Opérateur de Schrödinger pour un champ magnétique constant sur l'espace euclidien à deux dimensions
Operators on differential forms for Lie transformation groups.
Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles
Let be a principal bundle of frames with the structure group . It is shown that the variational problem, defined by -invariant Lagrangian on , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.