  In general relativity, the gravitational potential is represented by the
Levi-Civita connection, the only symmetric connection preserving the metric. On
a differentiable manifold, a metric identifies with an orthogonal structure,
defined as a Lorentz reduction of the frame bundle. The Levi-Civita connection
appears as the only symmetric connection preserving the reduction. This paper
presents generalization of this process to other aproaches of gravitation: Weyl
structure with Weyl connections, teleparallel structures with Weitzenbock
connections, unimodular structure, similarly appear as frame bundle reductions,
with preserving connections. To each subgroup H of the linear group GL
correspond reduced structures, or H-structures. They are subbundles of the
frame bundle (with GL as principal group), with H as principal group. A linear
connection in a manifold M is a principal connection on the frame bundle. Given
a reduction, the corresponding preserving connections on M are the linear
connections which preserve it. I also show that the time gauge used in the 3+1
formalism for general relativity similarly appears as the result of a bundle
reduction.
