Abstract
On manifolds with the pseudogroup structure of the group of projective transformations there are linear differential operators between certain spaces of tensor fields, the analogue for projective structures of the affine covariant derivative; such operators have played an important role in connection with the Eichler cohomology groups on one-dimensional complex manifolds. This paper contains a discussion of such operators of first- or second-order on two-dimensional complex manifolds, indicating the invariance properties involved and the corresponding exact sequences leading to generalizations of the Eichler cohomology groups.
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