On complete list of affine homogeneous surfaces of (?, 0)-types in the space ?sup class="a-plus-plus">3

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• 作者：A. V. Loboda ; A. V. Shipovskaya
• 关键词：complex space ; affine transformation ; homogeneous manifold ; vector field ; Lie algebra ; canonical equation
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：59
• 期：6
• 页码：62-67
• 全文大小：513 KB
• 参考文献：1.Cartan, E. “Sur la Géometrie Pseudoconforme des Hypersurfaces de Deux Variables Complèxes,-Ann. Math. Pura Appl. 11, No. 4, 17-0 (1932).MathSciNet
  2.Loboda, A. V. “Homogeneous Strictly Pseudoconvex Hypersurfaces in ?sup>3 with Two-Dimensional Isotropy Groups,-Sb.Math. 192, No. 12, 1741-761 (2001).View Article MATH MathSciNet
  3.Fels, G. and Kaup, W. “Classification of Levi Degenerate Homogeneous CR-Manifolds in Dimension 5,-Acta Math. 210, 1-2 (2008).View Article MathSciNet
  4.Beloshapka, V. K. and Kossovskiy, I. G. “Classification of Homogeneous CR-Manifolds in Dimension 4,-J. Math. Anal.Appl. 374, No. 2, 655-72 (2011).View Article MATH MathSciNet
  5.Loboda, A. V. and Khodarev, A. V. “A Family of Affinely Homogeneous Real Hypersurfaces of a Three-Dimensional Complex Space,-Russian Mathematics (Iz. VUZ) 47, No. 10, 35-7 (2003).MATH MathSciNet
  6.Loboda, A. V. and Nguyen, T. T. D. “On the Affine Homogeneity of Tubular Type Surfaces in ?sup>3,-Proc. Steklov Inst.Math. 279, 93-09 (2012).View Article MATH
  7.Loboda, A. V. “On Complete Description of Affine Homogeneous Real Hypersurfaces of Tubular Type of the Space ?sup>3,-in Proceedings of Voronezh Winter Math. School (VWMS-2013) (Voronezh, 2013), pp. 144-45.
  8.Atanov, A. V. Loboda, A. V. and Shipovskaya, A. V. “Affine Homogeneous Strictly Pseudoconvex Hypersurfaces of the Type (1/2, 0) in ?sup>3,-http://?arxiv.?org/?pdf/-401.-252v1.?pdf
  9.Nguyen, T. T. Z. “Affine-Homogeneous Real Hypersurfaces of Tube Type in ?sup>3,-Math. Notes 94, No. 2, 238-54 (2013).View Article MathSciNet
  10.Bishop, R. L. and Crittenden, R. J. Geometry of Manifolds (Academic Press, New York-London, 1964; Mir,Moscow, 1967).MATH
  
• 作者单位：A. V. Loboda (1)
  A. V. Shipovskaya (1)
  
  1. Voronezh State University of Architecture and Civil Engineering, ul. 20-Letiya Oktyabrya 84, Voronezh, 394006, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X

文摘

The problem of description of affine homogeneous real hypersurfaces in complex spaces is an important part of the problem of holomorphic classification of homogeneous manifolds, which has no complete solution till now, even in the 3-dimensional case. The method developed by the authors, based on affine canonical equations and techniques of matrix Lie algebras, allowed them earlier to obtain complete descriptions of two natural classes of affine homogeneous real hypersurfaces in the 3-dimensional complex space. In this paper, we present the complete description of one more class. The description includes examples already known and (obtained with the use of symbolic computations) Lie algebras corresponding to the other homogeneous manifolds belonging to the types under consideration. The main result of the paper is obtained by means of integration of these algebras.