Historical Comments on Monge’s Ellipsoid and the Configurations of Lines of Curvature on Surfaces

Jorge Sotomayor ; Ronaldo A. Garcia

Antiquitates Mathematicae, Tome 10 (2016), pp. 169-182.

Résumé

This is an essay on the historical landmarks leading to the study of principal confgurations on surfaces in R^3 , 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. Recent development concerning the space R^4 are mentioned. Two open problems are proposed at the end.

Détail

DOI : 10.14708/am.v10i0.1918

Classification : 53C12, 34D30, 53A05, 37C75, 01A99
Mots-clés : umbilic point, principal curvature cycle, principal curvature lines

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