, Volume 54, Issue 3, pp 323-332

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.

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.