A geometric approach to discrete connections on principal bundles

Abstract

This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form and discrete horizontal lift and studies some of their basic properties and relationships. An existence result for discrete connections on principal bundles equipped with appropriate Riemannian metrics is proved.

12 pages

References in corpus (1)

• Lagrangian reduction of discrete mechanical systems by stages

Cited by in corpus (5)

• Lagrangian reduction of discrete mechanical systems by stages
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• Discrete connections on principal bundles: the Discrete Atiyah Sequence
• The integration problem for principal connections
• Discrete Formulation for the dynamics of rods deforming in space