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.
@article{arxiv.1408.2806,
title = {Metric-Like Formulation Of the Spin-Three Gravity In Three Dimensions},
author = {Zhi-Qiang Guo},
journal= {arXiv preprint arXiv:1408.2806},
year = {2015}
}