Automorphisms of Tube Domains and Spherical Hypersurfaces

Sphericity of rigid hypersurfaces in ℂ2

“…Having the description of spherical tube hypersurfaces given in [2] in mind and taking into account the fact that for tubes the properties of umbilicity everywhere and sphericity coincide, we get the following result.…”

“…In the large, despite their Let R be a surface of this type. This means that in the vicinity of one of its points P(z0, w0) it is defined by the equation v = ~([z [2), where ~(t) is an analytic function.…”

“…w Classification of rigid spherical hypersurfaces In this section we discuss the rigid surfaces umbilical at each point that are given near the origin by an equation of the form (2), that is, Proof. Let us apply the transformation (4) to a surface F of the form (26).…”

Some invariants of tubular hypersurfaces in ℂ2

“…In view of [3], it is of interest to compare the list (2) with the list of spherical tubular hypersurfaces in C ~ . The base of each such tube is an a/fine image of one of the following curves: 2.…”

Аффинно-однородные вещественные гиперповерхности трубчатого типа в $\mathbb{C}^{3}$

“…Последнее уравнение пред-ставляет собой, как известно, сферическую трубчатую поверхность (см. [21], [22]). К построению примера (33) привело именно использование этого факта и аналогии со сферическими поверхностями в C 2 .…”