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ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3

Yıl 2016, Cilt: 4 Sayı: 2, 282 - 289, 01.10.2016

Şeyda Kılıçoğlu Süleyman Şenyurt Abdussamet Çalışkan

Öz

In this article we conceive eight ruled surfaces related to the evolute curve and involute . They are called as Frenet ruled surface and involutive Frenet ruled surfaces, cause of their generators are Frenet vector elds of evolute curve . First we give tangent vector elds of striction curves of all Frenet ruled surfaces and the tangent vector elds of striction curves of involutive Frenet ruled surfaces are given according to Frenet apparatus of evolute curve . Further we give only one matrix in which we can see sixteen position of these tangent vector elds, such that we can say there is six position the tangent vector elds are perpendicular.

Anahtar Kelimeler

Involute curve Striction curves Ruled surfaces Frenet ruled surface Involutive Frenet ruled surface

Kaynakça

  • [1] Do Carmo, M. P., Di erential Geometry of Curves and Surfaces. Prentice-Hall, sbn: 0-13- 212589-7, 1976.
  • [2] Graves L.K., Codimension one isometric immersions between Lorentz spaces. Trans. Amer. Math. Soc., 252, 367{392, 1979
  • [3] Gray, A., Modern Di erential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 205, 1997.
  • [4] Hacsalihoglu H.H., Di erential Geometry, Volume 1, Inonu University Publications, Malatya, 1994.
  • [5] Klcoglu S., On the B-scrolls with time-like directrix in 3-dimensional Minkowski Space. Beykent University Journal of Science and Technology, 2(2), 206-215, 2008.
  • [6] Klcoglu S., On the generalized B-scrolls with p th degree in n- dimensional Minkowski space and striction ( central spaces). Sakarya University Journal of science , 10(2), 15-29, 2008, issn:1301-3769.
  • [7] Klcoglu S., Senyurt S. and Hacsalihoglu H. H., On the Striction Curves of Involute and Bertrandian Frenet Ruled Surfaces in E3, Applied Mathematical Sciences, 2015, doi: 10.12988/ams.2015.59606, 9(142), 7081-7094.
  • [8] Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Ge- ometrie Contributions to Algebra and Geometry, 44(1), 203-212, 2003.
  • [9] Lipschutz, M., Di erential Geometry, Schaum's Outlines, 1969
  • [10] Senyurt, S. and Klcoglu S., On the di erential geometric elements of the involute ~D scroll, Advances in Applied Cli ord Algebras, Springer Basel, 25(4), 977-988, 2015, doi:10.1007/s00006-015-0535-z.

Yıl 2016, Cilt: 4 Sayı: 2, 282 - 289, 01.10.2016

Şeyda Kılıçoğlu Süleyman Şenyurt Abdussamet Çalışkan

Öz

Kaynakça

  • [1] Do Carmo, M. P., Di erential Geometry of Curves and Surfaces. Prentice-Hall, sbn: 0-13- 212589-7, 1976.
  • [2] Graves L.K., Codimension one isometric immersions between Lorentz spaces. Trans. Amer. Math. Soc., 252, 367{392, 1979
  • [3] Gray, A., Modern Di erential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 205, 1997.
  • [4] Hacsalihoglu H.H., Di erential Geometry, Volume 1, Inonu University Publications, Malatya, 1994.
  • [5] Klcoglu S., On the B-scrolls with time-like directrix in 3-dimensional Minkowski Space. Beykent University Journal of Science and Technology, 2(2), 206-215, 2008.
  • [6] Klcoglu S., On the generalized B-scrolls with p th degree in n- dimensional Minkowski space and striction ( central spaces). Sakarya University Journal of science , 10(2), 15-29, 2008, issn:1301-3769.
  • [7] Klcoglu S., Senyurt S. and Hacsalihoglu H. H., On the Striction Curves of Involute and Bertrandian Frenet Ruled Surfaces in E3, Applied Mathematical Sciences, 2015, doi: 10.12988/ams.2015.59606, 9(142), 7081-7094.
  • [8] Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Ge- ometrie Contributions to Algebra and Geometry, 44(1), 203-212, 2003.
  • [9] Lipschutz, M., Di erential Geometry, Schaum's Outlines, 1969
  • [10] Senyurt, S. and Klcoglu S., On the di erential geometric elements of the involute ~D scroll, Advances in Applied Cli ord Algebras, Springer Basel, 25(4), 977-988, 2015, doi:10.1007/s00006-015-0535-z.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Şeyda Kılıçoğlu

Süleyman Şenyurt Bu kişi benim

Abdussamet Çalışkan

Yayımlanma Tarihi 1 Ekim 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Kılıçoğlu, Ş., Şenyurt, S., & Çalışkan, A. (2016). ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3. Konuralp Journal of Mathematics, 4(2), 282-289.
AMA Kılıçoğlu Ş, Şenyurt S, Çalışkan A. ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3. Konuralp J. Math. Ekim 2016;4(2):282-289.
Chicago Kılıçoğlu, Şeyda, Süleyman Şenyurt, ve Abdussamet Çalışkan. “ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 282-89.
EndNote Kılıçoğlu Ş, Şenyurt S, Çalışkan A (01 Ekim 2016) ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3. Konuralp Journal of Mathematics 4 2 282–289.
IEEE Ş. Kılıçoğlu, S. Şenyurt, ve A. Çalışkan, “ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3”, Konuralp J. Math., c. 4, sy. 2, ss. 282–289, 2016.
ISNAD Kılıçoğlu, Şeyda vd. “ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3”. Konuralp Journal of Mathematics 4/2 (Ekim 2016), 282-289.
JAMA Kılıçoğlu Ş, Şenyurt S, Çalışkan A. ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3. Konuralp J. Math. 2016;4:282–289.
MLA Kılıçoğlu, Şeyda vd. “ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 282-9.
Vancouver Kılıçoğlu Ş, Şenyurt S, Çalışkan A. ON THE STRICTION CURVES OF INVOLUTIVE FRENET RULED SURFACES IN E3. Konuralp J. Math. 2016;4(2):282-9.
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