Abstract
We consider the 1|1-dimensional real superspace R-1|1 endowed with its standard contact structure defined by the 1-form a. The conformal Lie superalgebra K(1) acts on R1|1 as the Lie superalgebra of contact vector fields; it contains the Mobius superalgebra osp(1 | 2). We classify osp(1 | 2)-invariant linear differential operators from K(1) to D-lambda,D- mu;nu vanishing on osp(1 | 2), where D-lambda,D-mu;nu is the superspace of bilinear differential operators between the superspaces of weighted densities. This result allows us to compute the first differential osp(1 | 2)-relative cohomology of K(1) with coefficients in D-lambda,D-mu;nu. This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on RP1 acting on bilinear differential operators, Int. J. Geom. Methods Mod. Phys. 2(1) (2005) 23-40].