Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in \mathbb R³

2004/11/18 by Jorge Sotomayor, Sotomayor, Jorge
Mathematics · #34D30 #37C75 #53A05 #53C12 #Dynamical Systems (math.DS) #FOS: Mathematics #History and Overview (math.HO) #math.DS #math.HO #msc:34D30 #msc:37C75 #msc:53A05 #msc:53C12

paper · pdf · doi:10.48550/arxiv.math/0411403

10 pages, 5 figures

arxiv created 2004/11/18 · arxiv updated 2009/12/01

Abstract

This is an essay on the historical landmarks leading to the study of principal configurations on surfaces, their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative theory of differential equations, founded by Poincaré in 1881. Two open problems are proposed.

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