  We study Lyapunov exponents for flat bundles over hyperbolic curves defined
via parallel transport over the geodesic flow. We consider them as invariants
on the space of Hitchin representations and show that there is a gap between
any two consecutive Lyapunov exponents. Moreover we characterize the
uniformizing representation of the Riemann surface as the one with the extremal
gaps.
  The strategy of the proof is to relate Lyapunov exponents in the case of
Anosov representations to other invariants, where the gap result is already
available or where we can directly show it. In particular, firstly we relate
Lyapunov exponents to a foliated Lyapunov exponent associated to a foliation
H\"older isomorphic to the unstable foliation on the unitary tangent bundle of
a Riemann surface. Secondly, we relate them to the renormalized intersection
product in the setting of the thermodynamic formalism developed by Bridgeman,
Canary, Labourie and Sambarino.
