  The general relativity theory is redefined equivalently in almost Kahler
variables: symplectic form and canonical symplectic connection (distorted from
the Levi-Civita connection by a tensor constructed only from metric
coefficients and their derivatives). The fundamental geometric and physical
objects are uniquely determined in metric compatible form by a (pseudo)
Riemannian metric on a manifold enabled with a necessary type nonholonomic 2+2
distribution. Such nonholonomic symplectic variables allow us to formulate the
problem of quantizing Einstein gravity in terms of the A-model complexification
of almost complex structures on spacetime manifold, generalizing the
Gukov-Witten method, see arXiv:0809.0305. Quantizing the complexified model, we
derive a Hilbert space as a space of strings with two A-branes which for the
Einstein gravity theory are nonholonomic because of induced nonlinear
connection structures. Finally, we speculate on relation of such a method of
quantization to curve flows and solitonic hierarchies defined by Einstein
metrics on (pseudo) Riemannian spacetimes.
