Singularities of spherical surface in R4-Reference-Cited by-同舟云学术

Singularities of spherical surface in R4

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Liu Haiming¹,Hua Yuefeng¹,Li Wanzhen¹

Affiliation:

1. School of Mathematical Science, Mudanjiang Normal University , Mudanjiang , 157011 , China

Abstract

Abstract In this article, we mainly study the geometric properties of spherical surface of a curve on a hypersurface

\Sigma

in four-dimensional Euclidean space. We define a family of tangent height functions of a curve on

\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.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2024-0033/pdf

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