호남수학학술지 (Honam Mathematical Journal)

  • 제39권3호
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  • Pages.363-377
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  • 2017
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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ON GENERALIZED SPHERICAL SURFACES IN EUCLIDEAN SPACES

  • Bayram, Bengu (Department of Mathematics, Balikesir University) ;
  • Arslan, Kadri (Department of Mathematics, Uludag University) ;
  • Bulca, Betul (Department of Mathematics, Uludag University)
  • 투고 : 2017.02.10
  • 심사 : 2017.07.10
  • 발행 : 2017.09.25
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초록

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

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참고문헌

  1. K. Arslan, B. Bayram, B. Bulca and G. Ozturk, General Rotation Surfaces in $E^4$, Results. Math. 61 (2012), 315-327. https://doi.org/10.1007/s00025-011-0103-3
  2. K. Arslan, B. Bulca, and V. Milousheva, Meridian Surfaces in $\mathbb{E}^4$ with Pointwise 1-type Gauss Map, Bull. Korean Math. Soc. 51 (2014), 911-922. https://doi.org/10.4134/BKMS.2014.51.3.911
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