A. V. Loboda, “Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Trudy Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 114–142; Proc. Steklov Inst. Math., 235 (2001), 107

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 235, Pages 114–142 (Mi tm239)

This article is cited in 21 scientific papers (total in 21 papers)

Homogeneous Real Hypersurfaces in

C^{3}

$\mathbb C^3$ with Two-Dimensional Isotropy Groups

A. V. Loboda

Full-text PDF (337 kB) Citations (21)

References:

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Abstract: A local classification is constructed for real nonumbilic hypersurfaces of three-dimensional complex spaces that have sign-indefinite nondegenerate Levi forms and admit seven-dimensional transitive groups of local holomorphic transformations. A full (up to holomorphic equivalence) explicit description of such manifolds is presented. The basic tool used in this paper is the apparatus of local normal forms for the equations of the manifolds considered.

Received in March 2001

Bibliographic databases:

UDC: 517.55

Language: Russian

Citation: A. V. Loboda, “Homogeneous Real Hypersurfaces in

C^{3}

$\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Trudy Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 114–142; Proc. Steklov Inst. Math., 235 (2001), 107–135

Citation in format AMSBIB

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\by A.~V.~Loboda

\paper Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups

\inbook Analytic and geometric issues of complex analysis

\bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin

\serial Trudy Mat. Inst. Steklova

\yr 2001

\vol 235

\pages 114--142

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm239}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1886578}

\zmath{https://zbmath.org/?q=an:1023.32025}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2001

\vol 235

\pages 107--135

Linking options:

https://www.mathnet.ru/eng/tm239

https://www.mathnet.ru/eng/tm/v235/p114

This publication is cited in the following 21 articles:

A. V. Loboda, V. K. Kaverina, “About linear homogeneous hypersurfaces in $ \Bbb R^4 $”, Russian Math. (Iz. VUZ), 67:1 (2023), 43–63
A. V. Atanov, “Orbits of decomposable $7$-dimensional Lie algebras with $\mathfrak{sl}(2)$ subalgebra”, Ufa Math. J., 14:1 (2022), 1–19
A. V. Loboda, “On the Problem of Describing Holomorphically Homogeneous Real Hypersurfaces of Four-Dimensional Complex Spaces”, Proc. Steklov Inst. Math., 311 (2020), 180–198
Doubrov B., Medvedev A., The D., “Homogeneous Integrable Legendrian Contact Structures in Dimension Five”, J. Geom. Anal., 30:4 (2020), 3806–3858
Medvedev A. Schmalz G. Ezhov V., “On the Classification of Homogeneous Affine Tube Domains With Large Automorphism Groups in Arbitrary Dimensions”, Adv. Math., 364 (2020), 107028
A. V. Loboda, “Holomorphically homogeneous real hypersurfaces in $ \mathbb{C}^3$”, Trans. Moscow Math. Soc., 81:2 (2020), 169–228
R. S. Akopyan, A. V. Loboda, “On holomorphic realizations of 5-dimensional Lie algebras”, St. Petersburg Math. J., 31:6 (2020), 911–937
A. V. Atanov, A. V. Loboda, “Razlozhimye pyatimernye algebry Li v zadache o golomorfnoi odnorodnosti v $\mathbb{C}^3$”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 173, VINITI RAN, M., 2019, 86–115
A. V. Atanov, A. V. Loboda, V. I. Sukovykh, “On Holomorphic Homogeneity of Real Hypersurfaces of General Position in $\mathbb C^3$”, Proc. Steklov Inst. Math., 298 (2017), 13–34
Merker J., Sabzevari M., “Cartan Equivalence Problem for 5-Dimensional Bracket-Generating CR Manifolds in
$$\mathbb {C}^4$$
C 4”, J. Geom. Anal., 26:4 (2016), 3194–3251
T. T. D. Nguen, “Affine-Homogeneous Real Hypersurfaces of Tube Type in $\mathbb{C}^{3}$”, Math. Notes, 94:2 (2013), 238–254
A. V. Loboda, “Affinely Homogeneous Real Hypersurfaces of $\mathbb{C}^2$”, Funct. Anal. Appl., 47:2 (2013), 113–126
Beloshapka V.K., Kossovskiy I.G., “Classification of homogeneous CR-manifolds in dimension 4”, J Math Anal Appl, 374:2 (2011), 655–672
Beloshapka V.K., Kossovskiy I.G., “Homogeneous Hypersurfaces in C–3, Associated with a Model CR–Cubic”, Journal of Geometric Analysis, 20:3 (2010), 538–564
M. S. Danilov, A. V. Loboda, “Affine Homogeneity of Indefinite Real Hypersurfaces in the Space $\mathbb{C}^3$”, Math. Notes, 88:6 (2010), 827–843
A. M. Demin, A. V. Loboda, “An Example of a Two-Parameter Family of Affine Homogeneous Real Hypersurfaces in $\mathbb C^3$”, Math. Notes, 84:5 (2008), 737–740
Fels G., Kaup W., “Classification of Levi degenerate homogeneous CR–manifolds in dimension 5”, Acta Mathematica, 201:1 (2008), 1–82
I. G. Kossovskii, “On envelopes of holomorphy of model manifolds”, Izv. Math., 71:3 (2007), 545–571
A. V. Loboda, “On a Family of Lie Algebras Related to Homogeneous Surfaces”, Proc. Steklov Inst. Math., 253 (2006), 100–114
V. K. Beloshapka, “Symmetries of Real Hypersurfaces in Complex 3-Space”, Math. Notes, 78:2 (2005), 156–163

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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