J. Korean Math. Soc. 2017; 54(3): 999-1013
Online first article March 15, 2017 Printed May 1, 2017
https://doi.org/10.4134/JKMS.j160330
Copyright © The Korean Mathematical Society.
Kadri Arslan, Bet\"{u}l Bulca, and Didem Kosova
Uluda\u{g} University, Uluda\u{g} University, Uluda\u{g} University
In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean $ (n+1)$-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $ \mathbb{E}^{4}$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^{4}$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^{3}$ and $\mathbb{E}^{4}$, respectively.
Keywords: generalized tractrix, Gaussian curvature, rotational surface, Beltrami surface
MSC numbers: Primary 53C40, 53C42
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