Solution surfaces of Monge-Ampere equations

被引：7

作者：

Ishikawa, G

Morimoto, T

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[2] Nara Womens Univ, Dept Math, Nara 6308506, Japan

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2001年 / 14卷 / 02期

关键词：

Monge-Ampere equation; contact geometry; Legendre submanifold; projective duality; Hartman-Nirenberg's theorem; tangent developable; open umbrella;

D O I：

10.1016/S0926-2245(01)00033-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we examine the singularities of solution surfaces of Monge-Ampere equations and study their global and local effects on the solutions for certain kinds of equations in the framework of contact geometry. In particular, as a byproduct, we give a simple proof to the classical Hartman-Nirenberg's theorem by using the notion of projective duality and provide a new example of compact developable hypersurfaces in the real projective space RP4.

引用

页码：113 / 124

页数：12

共 27 条

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[2] THE FORM OF THE TANGENT-DEVELOPABLE AT POINTS OF ZERO TORSION ON SPACE-CURVES [J].