Branes and Calibrated Geometries

The vebrane worldvolume theory in eleven dimensions is known to contain BPS threebrane solitons which can also be interpreted as a vebrane whose worldvolume is wrapped around a Riemann surface. By considering con gurations of intersecting vebranes and hence intersecting threebrane solitons, we determine the Bogomol'nyi equations for more general BPS con gurations. We obtain di erential equations, generalising Cauchy-Riemann equations, which imply that the worldvolume of the vebrane is wrapped around a calibrated geometry.