Type IIA Killing spinors and calibrations

We consider the dimensional reduction of eleven dimensional supergravity to type IIA in ten dimensions, and study the conditions for supersymmetry in terms of p-form spinor bi-linears of the supersymmetry parameter. For a bosonic solution to be supersymmetric these p-forms must satisfy a set of differential relations, which we derive in full; the supersymmetry variations of the dilatino give a set of algebraic relations which are also derived. These results are then used to provide the generalized calibration conditions for some of the basic brane solutions, we also follow up a suggestion of Hackett-Jones and Smith and present a calibration condition for IIA supertubes. We find that a probe supertube satisfies this bound but does not saturate it, with the bound successfully accounting for the D0 charge of the supertube but not the string charge; we speculate that there should be a stronger calibration inequality than the one given.