Local isometry of the generalized helicoidal surfaces family in 4-space

Erhan Güler; Yusuf Yaylı

doi:10.26637/mjm1102/009

Abstract

In this paper, we define generalized helicoidal surface in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. We compute two normals and the curvatures of helicoidal surface. Finally, we obtain local isometry from generalized helicoidal surface to the generalized rotational surface by applying Bour's theorem in ${\mathbb{E}}^{4}$.

Keywords:

Euclidean 4-space, isometric deformation, Bour's theorem, helicoidal surface, mean curvature

Mathematics Subject Classification:

Computational Mathematics

Authors Imprint References Funding Related Articles Downloads

Erhan Güler Faculty of Sciences, Department of Mathematics, Bartın University, 74100 Bartın, Turkey.
Yusuf Yaylı aculty of Sciences, Department of Mathematics, Ankara University, 06100 Ankara, Turkey. https://orcid.org/0000-0003-4398-3855

Pages: 210-218
Date Published: 01-04-2023
Vol. 11 No. 02 (2023): Malaya Journal of Matematik (MJM)

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