Ruled Surfaces According to Parallel Trasport Frame in E4

DAMAR E., YÜKSEL N., KARACAN M. K.

15. Uluslararası Geometri Sempozyumu, Amasya, Türkiye, 3 - 06 Temmuz 2017, ss.1

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Amasya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.1
  • Erciyes Üniversitesi Adresli: Evet

Özet

Ruled Surfaces According to Parallel Trasport Frame in E4  

 

Esra DAMAR 1, Nural YÜKSEL2 and Murat Kemal KARACAN 3 

1 Department of Automotive Technologies,Hitit University,Çorum,Turkey,esradamar@hitit.edu.tr

2 Department of Mathematics, Erciyes University,Kayseri,Turkey,yukseln@erciyes.edu.tr

3 Department of Mathematics,Uşak University,Uşak,Turkey,murat.karacan@uşak.edu.tr
 


 

ABSTRACT

        In this paper, we studied the ruled surface generated by a straight line in parallel transport frame moving along a curve in four dimensional Euclidean space and we obtained Gaussian and mean curvatures.

        Some results and theorems related to be developable and Chen surfaces were given. As a result we gave a special example of ruled surfaces in E4.

 

        Key Words: Ruled surface, Gaussian curvature, Developable surface.

 

 

REFERENCES

  1. B.Bayram, B.Bulca, K.Arslan,G.Öztürk, Superconformal ruled surfaces in E4,Mathematical Communications 14(2009), 235-244.

  2. R. L.Bishop , There is More than One Way to Frame a Curve,The American Mathematical Monthly, 82(1975), 246-251.

  3. B. Y. Chen, Geometry of Submanifols, Dekker, New York, 1973.

  4. N.Yuksel, The ruled surfaces according to Bishop frame in minkowski 3-space, Abstract and Applied Analysis, 2013.