Open Mathematics (Aug 2024)

Singularities of spherical surface in R4

  • Liu Haiming,
  • Hua Yuefeng,
  • Li Wanzhen

DOI
https://doi.org/10.1515/math-2024-0033
Journal volume & issue
Vol. 22, no. 1
pp. 104513 – 720

Abstract

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In this article, we mainly study the geometric properties of spherical surface of a curve on a hypersurface Σ\Sigma in four-dimensional Euclidean space. We define a family of tangent height functions of a curve on Σ\Sigma as the main tool for research and combine the relevant knowledge of singularity theory. It is shown that there are three types of singularities of spherical surface, that is, in the local sense, the spherical surface is respectively diffeomorphic to the cuspidal edge, the swallowtail, and the cuspidal beaks. In addition, we give two examples of the spherical surface.

Keywords