  We study the Lyapunov spectrum of the geodesic flow of negatively curved
1/4-pinched Riemannian manifolds. We show that the space of metrics with simple
Lyapunov spectrum with respect to the equilibrium state of any H\"older
continuous potential is $C^k$ open and dense. The proof relies on a symbolic
coding of the flow to apply the simplicity criterion of Avila and Viana in
[AV07] and on perturbational results for $k$-jets of geodesic flows established
in [KT72].
