  We explore the class of triples (M, nabla, P) where M is a manifold, nabla is
an affine connection in M and P is a G-structure in M. Inside this class there
are infinitesimally homogeneous manifolds, characterized by having G-constant
curvature, torsion and inner torsion. For each matrix Lie group G subgroup of
GL(Rn) there is a class of infinitesimally homogeneous manifolds with structure
group G. In this paper we characterize the classes of infinitesimally
homogeneous manifolds for some specific values of the structure group G
including: identity group, finite groups, diagonal group, special linear group,
orthogonal group and unitary group.
