Araştırma Makalesi
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AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3

Yıl 2018, Cilt: 22 Sayı: 6, 1863 - 1867, 01.12.2018

İlim Kişi

https://doi.org/10.16984/saufenbilder.434801

Öz

We deal with AW(k)-type  Salkowski
(anti-Salkowski) curves with constant   in the Euclidean
3-space. We show that there is no AW(1)-type Salkowski curve and AW(1)-type
anti-Salkowski curve in . Also, we handle weak AW(2)-type and weak AW(3)-type
Salkowski (anti-Salkowski) curves. Also, we show that there is no weak AW(2)-type
Salkowski curve in .

Anahtar Kelimeler

AW(k)-type Salkowski Curve

Kaynakça

  • [1] K. Arslan and A. West, “Product submanifols with pointwise 3-planar normal sections,” Glasgow Math. J., vol.37, pp. 73-81, 1995.
  • [2] K. Arslan and C. Özgür, “Curves and surfaces of AW(k) type,” Geometry and topology of Submanifolds IX, World Scientific, 21-26, 1997.
  • [3] C. Özgür and F. Gezgin,.”On some curves of AW(k)-type,”. Differential Geometry-Dynamical Systems, vol. 7, pp. 74.80, 2005.
  • [4] B. Kılıç and K. Arslan, “On curves and surfaces of AW(k)-type,” BAÜ Fen Bil. Enst. Dergisi, vol. 6, no. 1, pp. 52-61, 2004.
  • [5] I. Kişi, S. Büyükkütük, Deepmala, and G. Öztürk, “AW(k)-type curves according to parallel transport frame in Euclidean space ,” Facta Universitaties, Series: Mathematics and Informatics, vol. 31, no. 4, pp. 885-905, 2016.
  • [6] I. Kişi and G. Öztürk, “AW(k)-type curves according to the Bishop frame,” arXiv:1305.3381v1 [math.DG], 2013.
  • [7] D. W. Yoon, “General helices of Aw(k)-type in the Lie group,” J. Appl. Math., pp.1-10, 2012.
  • [8] N. Chouaieb, A. Goriely, and J.H. Maddocks, “Helices,” PANS, 103, 9398.9403, 2006.
  • [9] A. A. Lucas and P. Lambin, “Diffraction by DNA, carbon nanotubes and other helical nanostructures,” Rep. Prog. Phys., vol. 68, 1181.1249, 2005.
  • [10] C. D. Toledo-Suarez, “On the arithmetic of fractal dimension using hyperhelices,” Chaos Solitons and Fractals, vol. 39, pp. 342.349, 2009.
  • [11] X. Yang, “High accuracy approximation of helices by quintic curve,” Comput. Aided Geometric Design, vol. 20, pp. 303.317, 2003.
  • [12] A. Gray, “Modern differential geometry of curves and surface,” CRS Press, Inc., 1993.
  • [13] H. Gluck, “Higher curvatures of curves in Euclidean space,” Amer. Math. Monthly, vol. 73, pp. 699-704, 1966.
  • [14] F. Klein and S. Lie, “Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren lin-earen transformationen in sich übergehen,” Math. Ann,. vol. 4, pp. 50-84, 1871.
  • [15] J. Monterde, “Curves with constant curvature ratios,” Bulletin of Mexican Mathematic Society,” vol. 13, pp. 177-186, 2007.
  • [16] G. Öztürk, K. Arslan, and H.H. Hacisalihoğlu, “A characterization of ccr-curves in ,” Proc. Estonian Acad. Sciences, vol. 57, pp. 217-224, 2008.
  • [17] E. Salkowski, “Zur transformation von raumkurven,” Math. Ann., vol. 66, pp. 517-557, 1909.
  • [18] A.T. Ali, “Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space,” Int. J. Open Problems Comp. Math., vol. 2, pp. 451.460, 2009.
  • [19] A.T. Ali, “Timelike Salkowski and anti-Salkowski curves in Minkowski 3-space,” J. Adv. Res. Dyn. Cont. Syst., vol. 2, pp. 17.26, 2010.
  • [20] F. Kaymaz and F. K. Aksoyak, “Some special curves and Manheim curves in three dimensional Euclidean space,” Mathematical Sciences and applications E-Notes, vol. 5, no. 1, pp. 34-39, 2017.
  • [21] J. Monterde, “Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion,” Computer Aided Geometric Design, vol. 26, no. 3, pp. 271-278, 2009.
  • [22] M. P. Do Carmo, “Differential geometry of curves and surfaces”, PrenticeHall, Englewood Cliffs, N. J. 1976.

Yıl 2018, Cilt: 22 Sayı: 6, 1863 - 1867, 01.12.2018

İlim Kişi

https://doi.org/10.16984/saufenbilder.434801

Öz

Kaynakça

  • [1] K. Arslan and A. West, “Product submanifols with pointwise 3-planar normal sections,” Glasgow Math. J., vol.37, pp. 73-81, 1995.
  • [2] K. Arslan and C. Özgür, “Curves and surfaces of AW(k) type,” Geometry and topology of Submanifolds IX, World Scientific, 21-26, 1997.
  • [3] C. Özgür and F. Gezgin,.”On some curves of AW(k)-type,”. Differential Geometry-Dynamical Systems, vol. 7, pp. 74.80, 2005.
  • [4] B. Kılıç and K. Arslan, “On curves and surfaces of AW(k)-type,” BAÜ Fen Bil. Enst. Dergisi, vol. 6, no. 1, pp. 52-61, 2004.
  • [5] I. Kişi, S. Büyükkütük, Deepmala, and G. Öztürk, “AW(k)-type curves according to parallel transport frame in Euclidean space ,” Facta Universitaties, Series: Mathematics and Informatics, vol. 31, no. 4, pp. 885-905, 2016.
  • [6] I. Kişi and G. Öztürk, “AW(k)-type curves according to the Bishop frame,” arXiv:1305.3381v1 [math.DG], 2013.
  • [7] D. W. Yoon, “General helices of Aw(k)-type in the Lie group,” J. Appl. Math., pp.1-10, 2012.
  • [8] N. Chouaieb, A. Goriely, and J.H. Maddocks, “Helices,” PANS, 103, 9398.9403, 2006.
  • [9] A. A. Lucas and P. Lambin, “Diffraction by DNA, carbon nanotubes and other helical nanostructures,” Rep. Prog. Phys., vol. 68, 1181.1249, 2005.
  • [10] C. D. Toledo-Suarez, “On the arithmetic of fractal dimension using hyperhelices,” Chaos Solitons and Fractals, vol. 39, pp. 342.349, 2009.
  • [11] X. Yang, “High accuracy approximation of helices by quintic curve,” Comput. Aided Geometric Design, vol. 20, pp. 303.317, 2003.
  • [12] A. Gray, “Modern differential geometry of curves and surface,” CRS Press, Inc., 1993.
  • [13] H. Gluck, “Higher curvatures of curves in Euclidean space,” Amer. Math. Monthly, vol. 73, pp. 699-704, 1966.
  • [14] F. Klein and S. Lie, “Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren lin-earen transformationen in sich übergehen,” Math. Ann,. vol. 4, pp. 50-84, 1871.
  • [15] J. Monterde, “Curves with constant curvature ratios,” Bulletin of Mexican Mathematic Society,” vol. 13, pp. 177-186, 2007.
  • [16] G. Öztürk, K. Arslan, and H.H. Hacisalihoğlu, “A characterization of ccr-curves in ,” Proc. Estonian Acad. Sciences, vol. 57, pp. 217-224, 2008.
  • [17] E. Salkowski, “Zur transformation von raumkurven,” Math. Ann., vol. 66, pp. 517-557, 1909.
  • [18] A.T. Ali, “Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space,” Int. J. Open Problems Comp. Math., vol. 2, pp. 451.460, 2009.
  • [19] A.T. Ali, “Timelike Salkowski and anti-Salkowski curves in Minkowski 3-space,” J. Adv. Res. Dyn. Cont. Syst., vol. 2, pp. 17.26, 2010.
  • [20] F. Kaymaz and F. K. Aksoyak, “Some special curves and Manheim curves in three dimensional Euclidean space,” Mathematical Sciences and applications E-Notes, vol. 5, no. 1, pp. 34-39, 2017.
  • [21] J. Monterde, “Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion,” Computer Aided Geometric Design, vol. 26, no. 3, pp. 271-278, 2009.
  • [22] M. P. Do Carmo, “Differential geometry of curves and surfaces”, PrenticeHall, Englewood Cliffs, N. J. 1976.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

İlim Kişi 0000-0003-2557-9023

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 19 Haziran 2018
Kabul Tarihi 5 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 6

Kaynak Göster

APA Kişi, İ. (2018). AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3. Sakarya University Journal of Science, 22(6), 1863-1867. https://doi.org/10.16984/saufenbilder.434801
AMA Kişi İ. AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3. SAUJS. Aralık 2018;22(6):1863-1867. doi:10.16984/saufenbilder.434801
Chicago Kişi, İlim. “AW(k)-Type Salkowski Curves in Euclidean 3-Space IE^3”. Sakarya University Journal of Science 22, sy. 6 (Aralık 2018): 1863-67. https://doi.org/10.16984/saufenbilder.434801.
EndNote Kişi İ (01 Aralık 2018) AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3. Sakarya University Journal of Science 22 6 1863–1867.
IEEE İ. Kişi, “AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3”, SAUJS, c. 22, sy. 6, ss. 1863–1867, 2018, doi: 10.16984/saufenbilder.434801.
ISNAD Kişi, İlim. “AW(k)-Type Salkowski Curves in Euclidean 3-Space IE^3”. Sakarya University Journal of Science 22/6 (Aralık 2018), 1863-1867. https://doi.org/10.16984/saufenbilder.434801.
JAMA Kişi İ. AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3. SAUJS. 2018;22:1863–1867.
MLA Kişi, İlim. “AW(k)-Type Salkowski Curves in Euclidean 3-Space IE^3”. Sakarya University Journal of Science, c. 22, sy. 6, 2018, ss. 1863-7, doi:10.16984/saufenbilder.434801.
Vancouver Kişi İ. AW(k)-type Salkowski Curves in Euclidean 3-Space IE^3. SAUJS. 2018;22(6):1863-7.
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