
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
Mathematics - Differential Geometry, Matemática, Principal bundle, FOS: Physical sciences, Mathematical Physics (math-ph), Differential Geometry (math.DG), Connection, FOS: Mathematics, Discrete dynamical system, 53B15, 53C05 (Primary) 37J15, 70G45 (Secondary), Ciencias Exactas, Mathematical Physics, Reduction, Symmetries
Mathematics - Differential Geometry, Matemática, Principal bundle, FOS: Physical sciences, Mathematical Physics (math-ph), Differential Geometry (math.DG), Connection, FOS: Mathematics, Discrete dynamical system, 53B15, 53C05 (Primary) 37J15, 70G45 (Secondary), Ciencias Exactas, Mathematical Physics, Reduction, Symmetries
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