An upper bound for the rational topological complexity of a family of elliptic spaces

In this work, we show that, for any simply-connected elliptic space $S$ admitting a pure minimal Sullivan model with a differential of constant length, we have ${\mathrm{T}\mathrm{C}}_0(S)\le 2{\mathrm{c}\mathrm{a}\mathrm{t}}_0(S)+{\chi }_{\pi }(S)$ where ${\chi }_{\pi }(S)$ is the homotopy characteristic. This is a consequence of a structure theorem for this type of models, which is actually our main result.