2020/09/11 by Jorge Sotomayor, Sotomayor, Jorge
Computer Science · Mathematics · Physics and Astronomy · #34D30 #37C75 #53A05 #53C12 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #History and Overview (math.HO) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2009.05638
openalex publication_date 2020/09/11 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This evocative essay focuses on some landmarks that led the author to the\nstudy of principal curvature configurations on surfaces in mathbb R3, their\nstructural stability and generic properties. The starting point was an\nencounter with the book of D. Struik and the reading of the references to the\nworks of Euler, Monge and Darboux found there. The concatenation of these\nreferences with the work of Peixoto, 1962, on differential equations on\nsurfaces, was a crucial second step. The circumstances of the convergence\ntoward the theorems of Guti 'errez and Sotomayor, 1982 - 1983, are recounted\nhere. The above 1982 - 1983 theorems are pointed out as the first encounter\nbetween the line of thought disclosed from the works of Monge, 1796, Dupin,\n1815, and Darboux, 1896, with that transpiring from the achievements of\nPoincar 'e, 1881, Andronov - Pontrjagin, 1937, and Peixoto, 1962. Some\nmathematical developments sprouting from the 1982 - 1983 works are mentioned on\nthe final section of this essay.\n