Infinite Deformed Groups and Their Geometrical and Physical Applications

In this article we give the realization of the Klein’s Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of bundles with use of idea of groups deformations. We also show that infinite deformed groups give a group-theoretic description of gauge fields (gravitational field with its metric or vierbein part similarly to gauge fields of internal symmetry) which is alternative for their geometrical interpretation.