[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160766

BOUR'S THEOREM IN 4-DIMENSIONAL EUCLIDEAN SPACE

Hieu, Doan The (College of Education Hue University)
Thang, Nguyen Ngoc (College of Education Hue University)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 2081-2089 More about this Journal

Abstract

In this paper we generalize 3-dimensional Bour's Theorem to the case of 4-dimension. We proved that a helicoidal surface in $\mathbb{R}^4$ is isometric to a family of surfaces of revolution in $\mathbb{R}^4$ in such a way that helices on the helicoidal surface correspond to parallel circles on the surfaces of revolution. Moreover, if the surfaces are required further to have the same Gauss map, then they are hyperplanar and minimal. Parametrizations for such minimal surfaces are given explicitly.

Keywords

Bour's theorem; helicoidal surface; surface of revolution; Gauss map; minimal surface;

Citations & Related Records

Reference

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