Work

Plane Curves with Proportional Affine and Euclidean Curvatures

Year: 2026

Type: article

Abstract: In this paper, we obtain all the locally convex plane curves with proportional curvatures (Euclidean and affine). The analysis is performed from a special second order differential equation that, in appropriated coordinates, and using the support function the problem is reduced to the properties of a periodic linear nonhomogeneous second differential equation of the type $$y''+y=a(t), \; a(t+2\pi )=a(t)$$ y ′ ′ + y = a ( t ) , a ( t + 2 π ) = a ( t ) .

Source: Qualitative Theory of Dynamical Systems

DOI: 10.1007/s12346-026-01475-3

Authors: Ronaldo A. Garcia, Armengol Gasull

Institutions: Universidade Federal de Goiás, Universitat Autònoma de Barcelona

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Universidade Federal de Goiás, Agencia Estatal de Investigación