Normal forms of the Whitney umbrella with respect to the contact group preserving a cone (Q1392341)

The purpose of this paper is to classify germs of mappings \(f:(R^2,0)\to (R^3,0)\) with respect to the contact group \({\mathcal K}_{\mathcal C}\), where \({\mathcal C}\) is a usual cone with vertex at zero. Additonally, the author assumes that the image of \(f\) is the well-known Whitney umbrella. The main result is connected with the following papers of \textit{J. Damon} [Lect. Notes Math. 1462, 93-121 (1991; Zbl 0822.32005)] and of \textit{D. Mond} [Proc. Lond. Math. Soc., III. Ser. 50, 333-369 (1985; Zbl 0557.58006)].