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October 2012 Geometric characterization of Monge-Ampère equations
Atsushi YANO
Hokkaido Math. J. 41(3): 409-440 (October 2012). DOI: 10.14492/hokmj/1351086222


It is well known that a Monge-Ampère equation can be expressed in terms of exterior differential system—Monge-Ampère system, which is the ideal generated algebraically by a contact form and a 2-form and its exterior derivatives on a 5-dimensional contact manifold, and the system is independent of the choice of coordinate system. On the other hand, a single second order partial differential equation of one unknown function with two independent variables corresponds to the differential system on a hypersurface of Lagrange-Grassmann bundle over a 5-dimensional contact manifold obtained by restricting its canonical system to the hypersurface. We observe relations between Monge characteristic systems of Monge-Ampère equation and those of Monge-Ampère system and particularly analyze structure equations of those systems. This observation leads to the result—to characterize Monge-Ampère equation by the property that the certain differential system defined from the Monge characteristic system drops down to the contact manifold.


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Atsushi YANO. "Geometric characterization of Monge-Ampère equations." Hokkaido Math. J. 41 (3) 409 - 440, October 2012.


Published: October 2012
First available in Project Euclid: 24 October 2012

zbMATH: 1256.58001
MathSciNet: MR3012457
Digital Object Identifier: 10.14492/hokmj/1351086222

Primary: 58A15
Secondary: 53D10

Keywords: Differential system , exterior differential system , Goursat equation , Monge characteristic system , Monge-Ampere equation , partial differential equation

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics


Vol.41 • No. 3 • October 2012
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