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

Jorge Sotomayor, and Ronaldo A. Garcia. "Historical Comments on Monge’s Ellipsoid and the Configurations of Lines of Curvature on Surfaces." Antiquitates Mathematicae 10 (2016): null. <http://eudml.org/doc/293278>.

@article{JorgeSotomayor2016,
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.},
author = {Jorge Sotomayor, Ronaldo A. Garcia},
journal = {Antiquitates Mathematicae},
keywords = {umbilic point, principal curvature cycle, principal curvature lines},
language = {eng},
pages = {null},
title = {Historical Comments on Monge’s Ellipsoid and the Configurations of Lines of Curvature on Surfaces},
url = {http://eudml.org/doc/293278},
volume = {10},
year = {2016},
}

TY - JOUR
AU - Jorge Sotomayor
AU - Ronaldo A. Garcia
TI - Historical Comments on Monge’s Ellipsoid and the Configurations of Lines of Curvature on Surfaces
JO - Antiquitates Mathematicae
PY - 2016
VL - 10
SP - null
AB - 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.
LA - eng
KW - umbilic point, principal curvature cycle, principal curvature lines
UR - http://eudml.org/doc/293278
ER -