Geometry of N=1 supergravity in (mn/m+n)-dimensional superspace

A class of N=1 supergravity theories in (mn/m+n)-dimensional superspaces is proposed for arbitrary natural numbers m and n, which includes the minimal N=1, D=4 supergravity in the Ogievetsky-Sokachev version corresponding to m=n=2. All geometric objects (connections, torsion, and curvature tensors) are expressed in terms of an mn-dimensional superfield. An invariant action for every N=1 supergravity theory from the constructed class is found