Castrillón López, MarcoRodríguez Abella, Álvaro2023-06-222023-06-222022https://hdl.handle.net/20.500.14352/71699In this work, generalized principal bundles modelled by Lie group bundle actions are investigated.In particular, definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together with the analysis of their existence and their main properties. The final part gives some examples. In particular, since this research was initially originated by some problems on geometric reduction of gauge field theories, we revisit the classical Utiyama Theorem from the perspective investigated in the article.engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articleopen access514.77Ehresmann connectionFiberwise actionLie group bundleParallel transportGeneralized principal bundleUtiyama TheoremGeometría diferencialGrupos (Matemáticas)1204.04 Geometría Diferencial