Open membranes in a constant C-field background and non-commutative boundary strings

We investigate the dynamics of open membrane boundaries in a constant C-fie ld background. We follow the analysis for open strings in a B-field backgro und, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boun daries are one-dimensional strings, so we face a new type of noncommutativi ty, that is, non-commutative strings.