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      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

       

      E M El-Kholy1 El-Said R Lashin2 Salama N Daoud2

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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