  In 1992, Hitchin used his theory of Higgs bundles to construct an important
family of representations of the fundamental group of a closed, oriented
surface of genus at least two into the split real form of a complex adjoint
simple Lie group. These Hitchin representations comprise a component of the
space of conjugacy classes of all such representations and are deformations of
the irreducible Fuchsian representations which uniformize the surface. For any
choice of marked complex structure on the surface and any Hitchin
representation, we show that the corresponding equivariant harmonic map from
the universal cover into the symmetric space is an immersion. Pulling back the
Riemannian metric on the symmetric space, we construct a map from the space of
Hitchin representations to the space of isotopy classes of Riemannian metrics
on the surface. As an application of this procedure, we obtain a new lower
bound on the exponential growth rate of orbits in the symmetric space under the
action of the image of a Hitchin representation.
