In this paper the authors give a topological classification of finitely determined weighted homogeneous map germs \(f:(\mathbb R^3,0)\to (\mathbb R^3,0)\) with 2-jet equivalent to \((x,y,xz)\). For this the authors use techniques developed in their previous paper [J. A. Moya-Pérez and J. J. Nuño-Ballesteros, “Gauss words and the topology of map germs from \(\mathbb R^3\) to \(\mathbb R^3\)”, {http://www.uv.es/nuno/Preprints.htm}] where they defined the Gauss paragraph as the collection of Gauss words of the discriminant of the link and the complement of the singular set of the link in the preimage of the discriminant. The link is obtained by taking the intersection of the image of \(f\) with a small enough sphere centered at the origin of \(\mathbb R^3\) and is a stable map from \(S^2\) to \(S^2\). They proved that if the singular sets are smooth and non empty outside the origin, two map germs are topologically equivalent if and only if their links are topologically equivalent, which is characterised by the equivalence of their Gauss paragraphs.
Finally, they classify all 2-ruled map germs from \(\mathbb R^3\) to \(\mathbb R^3\). These are obtained by moving a plane along a curve in \(\mathbb R^3\) and their discriminants are ruled surfaces.