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Mat. Zametki, 1996, Volume 59, Issue 2, Pages 211–223 (Mi mz1708)  

This article is cited in 11 scientific papers (total in 11 papers)

Some invariants of tubular hypersurfaces in $\mathbb C^2$

A. V. Loboda

Voronezh State Academy of Building and Architecture

Abstract: Holomorphic invariants of tubular hypersurfaces (tubes) over plane analytic curves are treated. Nonspherical Levi nondegenerate tubes over affine homogeneous curves are studied. Such surfaces are shown to be holomorphically equivalent if and only if they are affinely equivalent. Two problems concerning the description of locally specified homogeneous hypersurfaces in $\mathbb C^2$ are posed. The construction of the invariants is based on the reduction of the equation of a tubular hypersurface to Moser normal form. Some properties of this reduction are discussed.

DOI: https://doi.org/10.4213/mzm1708

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English version:
Mathematical Notes, 1996, 59:2, 148–157

Bibliographic databases:

UDC: 517.55
Received: 25.01.1995

Citation: A. V. Loboda, “Some invariants of tubular hypersurfaces in $\mathbb C^2$”, Mat. Zametki, 59:2 (1996), 211–223; Math. Notes, 59:2 (1996), 148–157

Citation in format AMSBIB
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\by A.~V.~Loboda
\paper Some invariants of tubular hypersurfaces in $\mathbb C^2$
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\yr 1996
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\pages 211--223
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\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 2
\pages 148--157
\crossref{https://doi.org/10.1007/BF02310954}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. N. Guzeev, A. V. Loboda, “Holomorphic invariants of logarithmic spirals”, Russian Math. (Iz. VUZ), 42:2 (1998), 13–16  mathnet  mathscinet  zmath
    2. A. V. Loboda, “Different definitions of homogeneity of real hypersurfaces in $\mathbb C^2$”, Math. Notes, 64:6 (1998), 761–766  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. V. Loboda, “Local Description of Homogeneous Real Hypersurfaces of the Two-Dimensional Complex Space in Terms of Their Normal Equations”, Funct. Anal. Appl., 34:2 (2000), 106–113  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. V. Loboda, “Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Proc. Steklov Inst. Math., 235 (2001), 107–135  mathnet  mathscinet  zmath
    5. R. N. Guzeev, A. V. Loboda, “On normal equations of affinely homogeneous convex surfaces of the space $\mathbb R^3$”, Russian Math. (Iz. VUZ), 45:3 (2001), 23–30  mathnet  mathscinet  zmath
    6. A. V. Loboda, “Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups”, Sb. Math., 192:12 (2001), 1741–1761  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Loboda, AV, “Each holomorphically homogeneous tube in C-2 has an affine-homogeneous base”, Siberian Mathematical Journal, 42:6 (2001), 1111  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    8. 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  mathnet  crossref  crossref  mathscinet  isi
    9. A. V. Loboda, “Affinely Homogeneous Real Hypersurfaces of $\mathbb{C}^2$”, Funct. Anal. Appl., 47:2 (2013), 113–126  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. Ezhov V., Kolar M., Schmalz G., “Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2”, Indiana Univ. Math. J., 62:1 (2013), 1–32  crossref  mathscinet  zmath  isi  scopus  scopus
    11. A. V. Loboda, “O razmernostyakh grupp affinnykh preobrazovanii, tranzitivno deistvuyuschikh na veschestvennykh giperpoverkhnostyakh v $\Bbb C^3$”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 4(23), 11–35  mathnet
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