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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 279, Pages 102–119
(Mi tm3427)
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This article is cited in 8 scientific papers (total in 8 papers)
On the affine homogeneity of tubular type surfaces in $\mathbb C^3$
A. V. Loboda, T. T. D. Nguyễn Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia
Abstract:
We present a systematic approach to solving the problem of affine homogeneity of real hypersurfaces in the three-dimensional complex space. This question is an important part of the general problem of holomorphic classification of homogeneous real hypersurfaces in three-dimensional complex spaces. In contrast to the two-dimensional case, the whole problem (just as its affine part) has not yet been fully studied, although there exist a large number of examples of homogeneous manifolds. We study only the class of tubular type surfaces, which is defined by conditions imposed on the $2$-jet of their canonical equations and generalizes the class of tube manifolds. We discuss the procedure of describing all matrix Lie algebras corresponding to the homogeneous manifolds under consideration. In the class that we study, we distinguish four cases depending on the third-order Taylor coefficients of the canonical equations; in three of these cases, the Lie algebras and the corresponding affine homogeneous surfaces are completely described. The key point of the proposed approach is the solution of a large system of quadratic equations that corresponds to each of the homogeneous surfaces.
Received in April 2012
Citation:
A. V. Loboda, T. T. D. Nguyẽn, “On the affine homogeneity of tubular type surfaces in $\mathbb C^3$”, Analytic and geometric issues of complex analysis, Collected papers, Trudy Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 102–119; Proc. Steklov Inst. Math., 279 (2012), 93–109
Linking options:
https://www.mathnet.ru/eng/tm3427 https://www.mathnet.ru/eng/tm/v279/p102
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