Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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TUBULAR SURFACES WITH MODIFIED ORTHOGONAL FRAME IN EUCLIDEAN 3-SPACE

  • Akyigit, Mahmut (Department of Mathematics, Faculty of Arts and Sciences, Sakarya University) ;
  • Eren, Kemal (Department of Mathematics, Faculty of Arts and Sciences, Sakarya University) ;
  • Kosal, Hidayet Huda (Department of Mathematics, Faculty of Arts and Sciences, Sakarya University)
  • Received : 2021.03.19
  • Accepted : 2021.06.03
  • Published : 2021.09.25
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Abstract

In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.

Keywords

References

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