Vol 10 (2016) , 169-182

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

Jorge Sotomayor, Ronaldo A. Garcia

Digital Object Identifier (DOI): 10.14708/am.v10i0.1918

Abstract

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.

Keywords: umbilic point, principal curvature cycle, principal curvature lines

Subject classification: 53C12, 34D30, 53A05, 37C75, 01A99

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