Calibrated cycles and T-duality

For a subclass of Hitchin's generalised geometries, we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition, these generalised calibrated cycles minimise a functional occurring as D-brane energy in type II string theories, involving both NS-NS- and R-R-fields. The central result shows generalised calibrated cycles to be exchanged under T-duality