Metric-Like Formulation Of the Spin-Three Gravity In Three Dimensions
  We provide a metric-like formulation of the spin-3 gravity in three dimensions. It is shown that the Chern-Simons formulation of the spin-3 gravity can be reformulated as a Einstein-Cartan-Sciama-Kibble theory coupled with the higher-spin matter fields. A duality-like transformation is also identified from this metric-like formulation. 
Zhi-Qiang Guo
hep-th gr-qc