Vol. 319, No. 1, 2022

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On the multiplicity of umbilic points

Marco Antônio do Couto Fernandes and Farid Tari

Vol. 319 (2022), No. 1, 99–127
Abstract

We introduce an invariant of umbilic points on surfaces in Euclidean or Minkowski 3-space that counts the maximum number of stable umbilic points they can split up under local deformations of the surfaces. We call that number the multiplicity of the umbilic point and establish its properties.

Keywords
umbilic points, lines of principal curvature, multiplicity, singularities
Mathematical Subject Classification
Primary: 53A05, 53A35, 53A55
Secondary: 58K05
Milestones
Received: 8 September 2021
Revised: 21 January 2022
Accepted: 21 January 2022
Published: 28 August 2022
Authors
Marco Antônio do Couto Fernandes
Instituto de Ciências Matemáticas e de Computação
University of São Paulo
São Carlos, SP
Brazil
Farid Tari
Instituto de Ciências Matemáticas e de Computação
University of Sao Paulo
São Carlos, SP
Brazil