  BiKaehler geometry is characterized by a Riemannian metric g_{ab} and two
covariantly constant generally non commuting complex structures K_+^a_b,
K_-^a_b, with respect to which g_{ab} is Hermitian. It is a particular case of
the biHermitian geometry of Gates, Hull and Roceck, the most general sigma
model target space geometry allowing for (2,2) world sheet supersymmetry. We
present a sigma model for biKaehler geometry that is topological in the
following sense: i) the action is invariant under a fermionic symmetry delta;
ii) delta is nilpotent on shell; iii) the action is delta--exact on shell up to
a topological term; iv) the resulting field theory depends only on a subset of
the target space geometrical data. The biKaehler sigma model is obtainable by
gauge fixing the Hitchin model with generalized Kaehler target space. It
further contains the customary A topological sigma model as a particular case.
However, it is not seemingly related to the (2,2) supersymmetric biKaehler
sigma model by twisting in general.
