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ON GENERALIZED ROTATIONAL SURFACES IN EUCLIDEAN SPACES

  • Arslan, Kadri (Department of Mathematics, Uludag University) ;
  • Bulca, Betul (Department of Mathematics, Uludag University) ;
  • Kosova, Didem (Department of Mathematics, Uludag University)
  • Received : 2016.05.06
  • Published : 2017.05.01

Abstract

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

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Cited by

  1. Rotational surfaces in higher dimensional Euclidean spaces 2016, https://doi.org/10.1007/s12215-016-0292-4
  2. Rotational submanifolds in Euclidean spaces vol.16, pp.02, 2019, https://doi.org/10.1142/S0219887819500294