On orbits of action of 5-dimensional non-solvable Lie algebras in three-dimensional complex space
- Authors: Atanov A.V.1, Kossovskiy I.G.2, Loboda A.V.3
-
Affiliations:
- Voronezh State University
- Masaryk University
- Voronezh State Technical University
- Issue: Vol 487, No 6 (2019)
- Pages: 607-610
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15949
- DOI: https://doi.org/10.31857/S0869-56524876607-610
- ID: 15949
Cite item
Full Text
Abstract
After the description by E. Cartan in 1932 holomorphically homogeneous real hypersurfaces of two-dimensional complex spaces, a similar study in the 3-dimensional case remains incomplete. In a series of works performed by several international teams of authors, the problem is reduced to describing homogeneous surfaces that are non-degenerate in Levi sense and have exactly 5-dimensional Lie algebras of holomorphic vector fields. In this paper, precisely such homogeneous surfaces are investigated. At the same time, a significant part of the extensive list of abstract 5-dimensional Lie algebras does not provide new examples of homogeneity. A complete description of the orbits of 5-dimensional non-solvable Lie algebras in a three-dimensional complex space, given in the paper, includes examples of new homogeneous hypersurfaces. The presented results bring to finish a large-scale scientific study of interest to various branches of mathematics.
About the authors
A. V. Atanov
Voronezh State University
Email: lobvgasu@yandex.ru
Russian Federation, 1, University square, Voronezh, 394063
I. G. Kossovskiy
Masaryk University
Email: lobvgasu@yandex.ru
Czech Republic, 617/9, Žerotínovo nám., Brno, 601 77
A. V. Loboda
Voronezh State Technical University
Author for correspondence.
Email: lobvgasu@yandex.ru
Russian Federation, 14, Moscowsky prospekt, Voronezh, 394026
References
- Лобода А. В. // Тр. Мат. ин-та РАН. 2001. Т. 235. С. 114-142.
- Fels G., Kaup W. // Acta Math. 2008. V. 201. P. 1-82.
- Doubrov В., Medvedev А., The D. // arXiv (2017) 1711.02389v1. http://arxiv.org/abs/1711.02389v1.
- Акопян Р. С., Лобода А. В. // Функц. анализ и его прил. 2019. Т. 53. № 2. С. 59-63.
- Атанов А. В., Лобода А. В. // Материалы международной конференции ВЗМШ 2019. 2019. С. 135-138.
- Мубаракзянов Г. М. // Изв. вузов. Матем. 1963. № 3. С. 99-106.
- Beloshapka V. K., Kossovskiy I. G. // J. Geom. Anal. 2010. V. 20. № 3. P. 538-564.
- Cartan E. // Ann. Math. Pura Appl. 1932. V. 11. № 4. P. 17-90.
- Fels G., Kaup W. // J. Reine Angew. Math. 2007. V. 604. P. 47-71.
- Chern S. S., Moser J. K. // Acta Math. 1974. V. 133. P. 219-271.
- Исаев А. В., Мищенко М. А. // Изв. АН СССР. Сер. матем. 1988. Т. 52. № 6. С. 1123-1153.
- Doubrov B., Komrakov B., Rabinovich M. // Geometry and Topology of Submanifolds, VIII. 1996. P. 168-178.