• Equi-Gaussian Curvature Folding

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/117/03/0293-0300

• # Keywords

Gaussian; curvature; folding; sphere; torus; polygon.

• # Abstract

In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds. We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case of equi-Gaussian curvature foldings, $f:M\to P_n$, of an orientable surface 𝑀 onto a polygon $P_n$ we prove that

(i) $f\in\mathcal{F}_{EG}(S^2)\Leftrightarrow n=3$

(ii) $f\in\mathcal{F}_{EG}(T^2)\Rightarrow n=4$

(iii) $f\in\mathcal{F}_{EG}(\# 2T^2)\Rightarrow n=5, 6$

and we generalize (iii) for $\# nT^2$.

• # Author Affiliations

1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
2. Department of Mathematics, Faculty of Science, El-Minufiya University, Shebeen El-Kom, Egypt

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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