Geometriae Dedicata

, Volume 54, Issue 3, pp 323–332

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

  • Dirce Kiyomi Hayashida Mochida
  • Maria Del Carmen Romero Fuster
  • Maria Aparecida Soares Ruas

DOI: 10.1007/BF01265348

Cite this article as:
Mochida, D.K.H., Romero Fuster, M.D.C. & Soares Ruas, M.A. Geom Dedicata (1995) 54: 323. doi:10.1007/BF01265348


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.

Mathematics Subject Classifications (1991)

Primary 58C27Secondary 53A05

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Dirce Kiyomi Hayashida Mochida
    • 1
  • Maria Del Carmen Romero Fuster
    • 2
  • Maria Aparecida Soares Ruas
    • 3
  1. 1.Departamento de MatemáticaUniversidade Federal de São CarlosSão Carlos, SPBrazil
  2. 2.Depto. de Geometria y TopologiaUniversidad de ValenciaValenciaSpain
  3. 3.Instituto de Ciências Matemáticas de São CarlosUniversidade de São Paulo, Departamento de MatemáticaSão Carlos, SPBrazil