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Umbilic singularities and lines of curvature on ellipsoids of ℝ4

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Abstract

The topological structure of the lines of principal curvature, the umbilic and partially umbilic singularities of all tridimensional ellipsoids of ℝ4 is described.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n Jardim Rosa Elze, 49100-000, São Cristóvão, SE, Brazil

    Débora Lopes

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010 Cidade Universitária, 05508-090, São Paulo, SP, Brazil

    Jorge Sotomayor

  3. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Caixa Postal 131, 74001-970, Goiânia, GO, Brazil

    Ronaldo Garcia

Authors
  1. Débora Lopes
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  2. Jorge Sotomayor
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  3. Ronaldo Garcia
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Correspondence to Ronaldo Garcia.

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Lopes, D., Sotomayor, J. & Garcia, R. Umbilic singularities and lines of curvature on ellipsoids of ℝ4 . Bull Braz Math Soc, New Series 45, 453–483 (2014). https://doi.org/10.1007/s00574-014-0058-6

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  • DOI: https://doi.org/10.1007/s00574-014-0058-6

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