We present the (1+1)-dimensional description of the algebraically special class of space-times of 4-dimensions. It is described by the (1+1)-dimensional Yang-Mills action interacting with matter fields, with diffeomorphisms of 2-surface as the gauge symmetry. Parts of the constraints are identified as the gauge fixing condition. We also show that the representations of $w_{ \infty}$-gravity appear naturally as special cases of this description, and discuss the geometry of $w_{ \infty}$-gravity in term of the fibre bundle.
Categories: hep-th gr-qc