On linear differential equations with reductive Galois group

Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive differential Galois group, we associate to it a projective variety. Connections such that their associated projective variety is curves can be classified, up to projective equivalence, using ruled surfaces. In particular, such a meromorphic connection is the pullback of a standard connection. This extends a similar result by Klein for second-order ordinary linear differential equations to a broader class of equations.