  For closed and connected subgroups G of SO(n), we study the energy functional
on the space of G-structures of a (compact) Riemannian manifold M, where
G-structures are considered as sections of the quotient bundle O(M)/G. Then, we
deduce the corresponding first and second variation formulae and the
characterising conditions for critical points by means of tools closely related
with the study of G-structures. In this direction, we show the role in the
energy functional played by the intrinsic torsion of the G-structure. Moreover,
we analyse the particular case G=U(n) for even-dimensional manifolds. This
leads to the study of harmonic almost Hermitian manifolds and harmonic maps
from M into O(M)/U(n).

Differential Geometry