Complex forms on supermanifolds
The authors introduce the notions \(r| s\) forms and an operation ``d'' on the domain of a supermanifold. The main results are: Theorem 1. The operation d is defined invariantly, carries forms of type \(r| s\) into forms of type \((r+1)| s\), and is a differential: \(d^ 2=0\). In the even case the differential constructed coincides with the differential d for exterior forms. Theorem 2. For the differential d constructed for \(r| s\) the Poincaré lemma holds, i.e., any closed form is locally exact.
scientific article; zbMATH DE number 4067898