Abstract
In this paper, we denote the Lie algebra of smooth vector fields on RP(1 )by V(RP1). This paper focuses on two parts. In the beginning, we determine the cohomology space of aff(1) with coefficients in D-tau,D-lambda,D-mu;nu. Afterward, we classify aff(1)-invariant fourth-linear differential operators from V(RP1) to D-tau,D-lambda,D-mu;nu vanishing on aff(1). This result enables us to compute the aff(1)-relative cohomology of V(RP1) with coefficients inD(tau,lambda,mu;nu).