Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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KILLING MAGNETIC FLUX SURFACES IN EUCLIDEAN 3-SPACE

  • Ozdemir, Zehra (Department of Mathematics, Faculty of Science and Arts, Amasya University) ;
  • Gok, Ismail (Department of Mathematics, Faculty of Science, University of Ankara) ;
  • Yayli, Yusuf (Department of Mathematics, Faculty of Science, University of Ankara) ;
  • Ekmekci, F. Nejat (Department of Mathematics, Faculty of Science, University of Ankara)
  • Received : 2018.10.18
  • Accepted : 2019.01.29
  • Published : 2019.06.25
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Abstract

In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.

Keywords

HNSHCY_2019_v41n2_329_f0001.png 이미지

FIGURE 1. Flux surface X(u,v)=(cos u, sin v, sin(cos 2v - cos 2u)3.

HNSHCY_2019_v41n2_329_f0002.png 이미지

FIGURE 2. X(u,v)=((2 + cos v) cosu, (2 + cos v) sinu, 2 sin v cos v.

HNSHCY_2019_v41n2_329_f0003.png 이미지

FIGURE 3. X(u,v)=((2 + cos v) cosu, (2 + cos v) sinu, v3 - 6v).

HNSHCY_2019_v41n2_329_f0004.png 이미지

FIGURE 4. X(u,v)=((2 + cos v) cosu, (2 + cos v) sinu, v2 + 4v).

HNSHCY_2019_v41n2_329_f0005.png 이미지

FIGURE 5. X(u,v)=((2 + cos v) cos u, (2 + cos v) sin u, v3 + 6v).

HNSHCY_2019_v41n2_329_f0006.png 이미지

FIGURE 6. Flux surface X(u,v)=($\sqrt{uv}$, sin(uv)3, 1/2 sin(2uv)).

HNSHCY_2019_v41n2_329_f0007.png 이미지

FIGURE 7. Flux surface and magnetic curves γ1(Black), γ2(Green) and γ3(Red) on this surface.

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