2005/01/24 by Jorge Sotomayor, Sotomayor, Jorge, Ronaldo Garcia +1
Mathematics · #34C23 #53A05 #58K25 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/0501422
openalex publication_date 2005/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3-space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable -- do not change topologically-- under small perturbations on the coefficients of the equations defining algebraic surfaces. This paper goes one step further and classifies the patterns of the most common and stable behaviors at the ends, present also in generic families of surfaces depending on one-parameter.