Abstract
We study the conditions to have supersymmetric D-branes on
general 
= 1 backgrounds with Ramond-Ramond fluxes. These
conditions can be written in terms of the two pure spinors
associated to the SU(3) × SU(3) structure on
TM⊕T⋆M, and can be split into two parts each
involving a different pure spinor. The first involves the integrable
pure spinor and requires the D-brane to wrap a generalised complex
submanifold with respect to the generalised complex structure
associated to it. The second contains the non-integrable pure spinor
and is related to the stability of the brane. The two conditions can
be rephrased as a generalised calibration condition for the
brane. The results preserve the generalised mirror symmetry relating
the type IIA and IIB backgrounds considered, giving further evidence
for this duality.
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