The Möbius geometry of hypersurfaces. II.
It is the second part of the paper [Mich. Math. J. 56, No. 3, 603--622 (2008; Zbl 1160.32005)] published by the author recently. The main theorem of the present article states: Let \(M^3 \subset {\mathbb C}^2\) be a non-Levi-flat, three times differentiable hypersurface, and let there is a constant \(\varepsilon\in {\mathbb C},\; |\varepsilon| \not= 0, 1,\) such that, for all \(p\in M\), \[ {\mathcal Q}_{r,p} = \varepsilon {\mathcal L}_{r,p}. \] Then \(M\) is contained in the image of \[ M_{\varepsilon} \equiv \left\{(z_1,z_2) : (z_1 + \overline{z}_1) + |z_2|^2 + {\mathrm{Re}} (\varepsilon z_2^2) = 0\right\} \] under an affine map of the form \(F(z) = A z + b\), where \(0 \not= \det A\in {\mathbb R}\).
scientific article; zbMATH DE number 5843849