Superbranes and Generic Curved Spacetime

Embedding of a bosonic and/or fermionic p-brane into a generic curved $D$-dimensional spacetime is considered. In contradistinction to the bosonic p-brane case, when there are no constraints on a generic curving whatsoever, the usual superbrane can be embedded into a curved spacetime of a restricted curving only. A generic curving is achieved by extending the odd sector of a superbrane as to transform w.r.t. $\overline{SL}(D,R)$, i.e. $\overline{Diff}(D,R)$ infinite-component spinorial representations. Relevant constructions in the D=3 case are considered.