Hypergraphs are a generalization of graphs where hyperedges are allowed to connect an arbitrary number of nodes. This provides a much more faithful representation in many real-life cases. We tackle the problem of node partitioning by extending the notion of Ricci curvature on graphs to hypergraphs. We introduce a novel method where we transport measures defined on the hyperedges such that nodes assigned to different communities have a high transportation distance. We extensively compare this method with a similar notion of Ricci flow defined on the clique expansion, demonstrating its enhanced sensitivity to the hypergraph structure, especially in the presence of large hyperedges. The two methods are complementary and together form a powerful and highly interpretable framework for community detection in hypergraphs.