This article is cited in 9 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.

UDC: 514.763

MSC: Primary 53C15, 53C12; Secondary 35J60

Received: 06.02.1997

DOI: 10.4213/sm370

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

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