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The geometry of surfaces in 4-space from a contact viewpoint

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Abstract

We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de São Carlos, 13560-905, São Carlos, SP, Brazil

    Dirce Kiyomi Hayashida Mochida

  2. Depto. de Geometria y Topologia, Universidad de Valencia, 46100, Valencia, Spain

    Maria Del Carmen Romero Fuster

  3. Instituto de Ciências Matemáticas de São Carlos, Universidade de São Paulo, Departamento de Matemática, 13560-970, São Carlos, SP, Brazil

    Maria Aparecida Soares Ruas

Authors
  1. Dirce Kiyomi Hayashida Mochida
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  2. Maria Del Carmen Romero Fuster
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  3. Maria Aparecida Soares Ruas
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Additional information

The research of the second author was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.

The research of the third author was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.

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Mochida, D.K.H., Romero Fuster, M.D.C. & Soares Ruas, M.A. The geometry of surfaces in 4-space from a contact viewpoint. Geom Dedicata 54, 323–332 (1995). https://doi.org/10.1007/BF01265348

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  • DOI: https://doi.org/10.1007/BF01265348

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