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 \({\rm TC}_0(S)\leq 2{\rm cat}_0(S)+\chi_{\pi}(S)\) 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.