Three-Jets Determinations of Normalized Proper Holomorphic Maps from \( \mathbb {H}_n\) into \(\mathbb {H}_{3n-2}\)

We derive the explicit formula for the normalized rational proper holomorphic maps of \(Rat({\mathbb H}_n, {\mathbb H}_{3n-2})\) $Rat({\mathbb{H}}_n,{\mathbb{H}}_{3n-2})$ . As a consequence, we prove that these maps are determined by their three jets.