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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 6, Pages 103–140 (Mi izv8145)  

This article is cited in 4 scientific papers (total in 4 papers)

The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$

J. Merkera, M. Sabzevarib

a Université Paris-Sud, Orsay cedex
b Shahrekord University, Iran

Abstract: We develop the Cartan equivalence problem for Levi-non-degenerate $\mathcal C^6$-smooth real hypersurfaces $M^3$ in $\mathbb C^2$ in great detail, performing all computations effectively in terms of local graphing functions. In particular, we present explicitly the unique (complex) essential invariant $\mathfrak{J}$ of the problem. Comparison with our previous joint results [1] shows that the Cartan–Tanaka geometry of these real hypersurfaces perfectly matches their biholomorphic equivalence.

Keywords: CR-manifolds, Levi non-degeneracy, essential torsions, $G$-structures, curvature tensor.

Funding Agency Grant Number
School of Mathematics, Institute for Research in Fundamental Sciences 91530040


DOI: https://doi.org/10.4213/im8145

Full text: PDF file (740 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:6, 1158–1194

Bibliographic databases:

UDC: 514.76
MSC: 32V40, 53C10
Received: 05.07.2013

Citation: J. Merker, M. Sabzevari, “The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$”, Izv. RAN. Ser. Mat., 78:6 (2014), 103–140; Izv. Math., 78:6 (2014), 1158–1194

Citation in format AMSBIB
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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. M. Sabzevari, “Moduli spaces of model real submanifolds: two alternative approaches”, Sci. China Math., 58:1 (2015), 2261–2278  crossref  mathscinet  zmath  isi  elib  scopus
    2. J. Merker, M. Sabzevari, “Cartan Equivalence Problem for 5-Dimensional Bracket-Generating CR Manifolds in $\mathbb {C}^4$”, J. Geom. Anal., 26:4 (2016), 3194–3251  crossref  mathscinet  zmath  isi  elib  scopus
    3. Sabzevari M., “Biholomorphic Equivalence to Totally Nondegenerate Model Cr Manifolds”, Ann. Mat. Pura Appl., 198:4 (2019), 1121–1163  crossref  isi
    4. Isaev A., Merker J., “on the Real-Analyticity of Rigid Spherical Hypersurfaces in C-2”, Proc. Amer. Math. Soc., 147:12 (2019), 5251–5256  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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