On analogues of B\"acklund theorem in affine differential geometry of surfaces

Abstract

We recall the well-known Chern-Terng theorem concerning affine minimal surfaces. Next we formulate some complementary (with transversal fields necessarily not parallel) affine B\"acklund theorem. We describe some geometrical conditions which imply the local symmetry of both induced connections. We give also some necessary and sufficient conditions under which the affine fundamental forms are proportional.