Supertubes and supercurves from M-ribbons

We construct 14 BPS configurations, ‘M-ribbons’, in M-theory on T2, which give the supertubes and supercurves in type IIA theory upon-dimensional reduction. These M-ribbons are generalized so as to be consistent with the SL(2,Z) modular transformation on T2. In terms of the type IIB theory, the generalized M-ribbons are interpreted as an SL(2,Z) duality family of super D-helix. It is also shown that the BPS M-ribbons must be straight in one direction.