This article is cited in 38 papers

Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups

A. V. Loboda

Voronezh State Academy of Building and Architecture

Abstract: Strictly pseudoconvex non-spherical hypersurfaces in 3-dimensional complex space that are homogeneous with respect to local Lie groups of holomorphic transformations are studied. The author proved earlier that a Lie group $\operatorname{Aut}M$ acting transitively on such a manifold $M$ has dimension at most 7.
A complete list of homogeneous surfaces such that $\operatorname{Aut}M$ has dimension precisely 7 (and the corresponding isotropy subgroup has dimension precisely 2) is given. The main tools used in the paper are local normal equations describing the manifolds under consideration.

UDC: 517.5

MSC: Primary 32V40, 53C30; Secondary 32M25

Received: 25.01.2001

DOI: 10.4213/sm614

 English version: Sbornik: Mathematics, 2001, 192:12, 1741–1761

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