  In this paper we study Holder continuous linear cocycles over transitive
Anosov diffeomorphisms. Under various conditions of relative pinching we
establish properties including existence and continuity of measurable invariant
sub-bundles and conformal structures. We use these results to obtain criteria
for cocycles to be isometric or conformal in terms of their periodic data. We
show that if the return maps at the periodic points are, in a sense, conformal
or isometric then so is the cocycle itself with respect to a Holder continuous
Riemannian metric.
