Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane

被引：9

作者：

Arnold, V ^{[1
]}

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris, France

[2] VA Steklov Math Inst, Moscow 117333, Russia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2005年 / 53卷 / 04期

关键词：

projective geometry; de Sitter world; symplectic algebra; Klein model;

D O I：

10.1016/j.geomphys.2004.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An isomorphism between the Lobachevsky and de Sitter's world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：421 / 427

页数：7