Displaying similar documents to “The Problem of Invariance for Covariant hamiltonians”

Natural operators in the view of Cartan geometries

Martin Panák (2003)

Archivum Mathematicum

Similarity:

We prove, that r -th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order ( 1 , 0 ) (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order r - 1 . On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem...

The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles

Charles-Michel Marle (2007)

Banach Center Publications

Similarity:

Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers,...

Connections on higher order principal prolongations

Vašík, Petr

Similarity:

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.