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Mat. Sb., 1998, Volume 189, Number 11, Pages 61–74 (Mi msb370)  

This article is cited in 8 scientific papers (total in 8 papers)

Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations

B. S. Kruglikov

M. V. Lomonosov Moscow State University

Abstract: Three related classification problems on four-manifolds are discussed. First, regular distributions are considered and described locally. After that a classification of almost complex structures of general position in terms of distributions is proposed. Finally, non-degenerate generalized Monge–Ampere equations are classified in terms of $\{e\}$-structures. Symplectic Lie algebras are also considered in an appendix.

DOI: https://doi.org/10.4213/sm370

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English version:
Sbornik: Mathematics, 1998, 189:11, 1643–1656

Bibliographic databases:

UDC: 514.763
MSC: Primary 53C15, 53C12; Secondary 35J60
Received: 06.02.1997

Citation: B. S. Kruglikov, “Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations”, Mat. Sb., 189:11 (1998), 61–74; Sb. Math., 189:11 (1998), 1643–1656

Citation in format AMSBIB
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\pages 61--74
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\pages 1643--1656
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Kushner, “Almost product structures and Monge-Ampère equations”, Lobachevskii J. Math., 23 (2006), 151–181  mathnet  mathscinet  zmath
    2. Marvan, M, “Differential invariants of generic hyperbolic Monge-Ampere equations”, Central European Journal of Mathematics, 5:1 (2007), 105  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. Tonejc, J, “Normal forms for almost complex structures”, International Journal of Mathematics, 19:3 (2008), 303  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Kushner, AG, “A contact linearization problem for Monge-Ampere equations and Laplace invariants”, Acta Applicandae Mathematicae, 101:1–3 (2008), 177  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. A. G. Kushner, “O privedenii uravnenii Monzha–Ampera k uravneniyu Eilera–Puassona”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 151, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2009, 60–71  mathnet  elib
    6. Kushner A.G., “Classification of Monge-Ampere Equations”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, 2009, 223–256  mathscinet  zmath  isi
    7. Kushner, AG, “On Contact Equivalence of Monge-AmpSre Equations to Linear Equations with Constant Coefficients”, Acta Applicandae Mathematicae, 109:1 (2010), 197  crossref  zmath  isi  scopus  scopus  scopus
    8. Zaitsev D., “Normal Forms for Nonintegrable Almost Cr Structures”, Am. J. Math., 134:4 (2012), 915–947  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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