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On the multiplicity
of umbilic points
Marco Antônio do Couto Fernandes and Farid Tari |
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Vol. 319 (2022), No. 1, 99–127
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Abstract |
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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
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Mathematical Subject Classification
Primary: 53A05, 53A35, 53A55
Secondary: 58K05
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Milestones
Received: 8 September 2021
Revised: 21 January 2022
Accepted: 21 January 2022
Published: 28 August 2022
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Authors |
| Marco Antônio do Couto Fernandes | |
| Instituto de Ciências Matemáticas e
de Computação University of São Paulo São Carlos, SP Brazil |
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| Farid Tari | |
| Instituto de Ciências Matemáticas e
de Computação University of Sao Paulo São Carlos, SP Brazil |
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