arXiv subjects
Publications and source records attributed to Serhiy E. Samokhvalov.
We show that finite parallel transports of vectors in Riemannian spaces, determined by the multiplication law in the deformed groups of diffeomorphisms, and sequences of infinitesimal parallel transports of vectors along geodesics are equivalent.
It is shown that a locally geometrical structure of arbitrarily curved Riemannian space is defined by a deformed group of its diffeomorphisms
We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain covariant derivatives, and structure functions - the curvature tensor.
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.