  In this article we initiate the study of 1+ 2 dimensional wave maps on a
curved spacetime in the low regularity setting. Our main result asserts that in
this context the wave maps equation is locally well-posed at almost critical
regularity.
  As a key part of the proof of this result, we generalize the classical
optimal bilinear L^2 estimates for the wave equation to variable coefficients,
by means of wave packet decompositions and characteristic energy estimates.
This allows us to iterate in a curved X^{s,b} space.
