A BRST-like operator for space with zero curvature but non-zero torsion tensor

A new type of BRST-like operatorQ has been constructed for spaces with zero Riemann curvature tensor but with non-zero torsion. It is invariant under local coordinate transformation, and its proof depends upon the validity of the first Bianchi identity. Also, there exists a supersymmetry associated withQ. Finally, the cohomology induced byQ has been investigated.