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This article is cited in 8 scientific papers (total in 8 papers)
Sphericity of rigid hypersurfaces in $\mathbb C^2$
A. V. Loboda Voronezh Engineering Building Academy
Abstract:
The sphericity of hypersurfaces in the space $\mathbb C^2_{z,w}$ (locally) representable by equations of the form $\operatorname{Im}v=F(z,\overline z)$ is discussed. Invoking the notion of Moser normal form, a necessary and sufficient condition for these surfaces to be spherical is constructed. It is a partial differential third-order equation for the function $\mu(z,\overline z)=F_{zz\overline z}/F_{z\overline z}$. The similarity between this equation and the sphericity criterion for tube hypersurfaces makes it possible to reduce the problem to the familiar description of spherical tubes. Reduction mappings are written out explicitly. As a particular case, a description of Reinhardt spherical surfaces defined by the equations $\operatorname{Im}w=\alpha(|z|^2)$ is given.
Received: 19.01.1996
Citation:
A. V. Loboda, “Sphericity of rigid hypersurfaces in $\mathbb C^2$”, Mat. Zametki, 62:3 (1997), 391–403; Math. Notes, 62:3 (1997), 329–338
Linking options:
https://www.mathnet.ru/eng/mzm1621https://doi.org/10.4213/mzm1621 https://www.mathnet.ru/eng/mzm/v62/i3/p391
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