  The existence of a new kind of branes for the open topological A-model is
argued by using the generalized complex geometry of Hitchin and the SYZ picture
of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the
normal direction of the brane and a new definition of generalized complex
submanifold. Using this definition, it is shown that there exists generalized
complex submanifolds which are isotropic in a symplectic manifold. For certain
target space manifolds this leads to isotropic A-branes, which should be
considered in addition to Lagrangian and coisotropic A-branes. The Fukaya
category should be enlarged with such branes, which might have interesting
consequences for the homological mirror symmetry of Kontsevich. The stability
condition for isotropic A-branes is studied using the worldsheet approach.
