Squares of Hamiltonian cycles in 3-uniform hypergraphs

We show that every $3$-uniform hypergraph $H=(V,E)$ with $\mathrm{\mid }V(H)\mathrm{\mid }=n$ and minimum pair degree at least $(4\mathrm{/}5+o(1))n$ contains a squared Hamiltonian cycle. This may be regarded as a first step towards a hypergraph version of the P'osa-Seymour conjecture.