Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in ${\mathbb R}^3$

Details Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in ${\mathbb R}^3$ Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in ${\mathbb R}^3$

2004-11-18

arxiv.org/abs/math/0411403v1

Mathematics

History and Overview

10 pages, 5 figures

Scientific paper

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
Poincar\'e in 1881. Two open problems are proposed.

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