Noncommutative 2-Dimensional Models of Gravity
  A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an intimate relation between noncommutative geometry on the one hand and classical gravity on the other. 
M. Buric and J. Madore