A new type of canal surface in Euclidean 4-space E^4

Year 2019, Volume: 23 Issue: 5, 801 - 809, 01.10.2019

İlim Kişi Günay Öztürk Kadri Arslan

https://doi.org/10.16984/saufenbilder.524471

Cited By: 3

Abstract

Bu çalışmada, E^4 4-boyutlu Öklid uzayında, merkez eğrisinin paralel öteleme çatısı vektörleri yardımıyla tanımlanan kanal yüzeyini örneği ile verdik. Bu yüzeyin eğrilik özelliklerini paralel öteleme çatısına göre eğrilik fonksiyonları cinsinden araştırdık. Daha sonra, Weingarten tipindeki kanal ve tüp yüzeyleri hakkında bazı sonuçlar verdik. Son olarak, bu tipteki yüzeylerin farklı yarıçap fonksiyonları için E^3 uzayındaki izdüşümlerini çizdirdik.

Keywords

Gaussian curvature, mean curvature, parallel transport frame, Weingarten surface

References

• [1] K. Arslan, B. (Kılıç) Bayram, B. Bulca, G. Öztürk, “On translation surfaces in 4-dimensional Euclidean space,” Acta et Commentationes Universitatis Tartuensis de Mathematica, vol. 20, no. 2, pp. 123-133, 2016.
• [2] K. Arslan, B. Bayram, B. Bulca, G. Öztürk, “Generalized rotation surfaces in ,” Results in Mathematics, vol. 61, pp. 315-327, 2012.
• [3] K. Arslan, B. Bulca, B. (Kılıç) Bayram, G. Öztürk, “Normal transport surfaces in Euclidean 4-space ,” Differential Geometry-Dynamical Systems, vol. 17, pp. 13-23, 2015.
• [4] P. Bayard and F. Sanchez-Bringas, “Geometric invariants of surfaces in ,” Topology and its Applications, vol. 159, no. 2, pp. 405-413, 2012.
• [5] B. Bayram, B. Bulca, K. Arslan, and G. Öztürk, “Superconformal ruled surfaces in ,” Mathematical Communications, vol. 14, pp. 235-244, 2009.
• [6] L.R. Bishop, “There is more than one way to frame a curve,” Amer. Math. Monthly, vol. 82, pp. 246-251, 1975.
• [7] B. Bulca, “A characterization of surfaces in ,” PhD, Uludag University, Bursa, Turkey, 2012.
• [8] B. Bulca and K. Arslan, “Surfaces given with the Monge patch in ,” Journal of Mathematical Physics, Analysis, Geometry, vol. 9, no. 4, pp. 435–447, 2013.
• [9] B. Bulca, K. Arslan, B. Bayram, and G. Öztürk, “Canal surfaces in 4-dimensional Euclidean space,” An International Journal of Optimization and Control: Theories and Applications, vol. 7, no. 1, pp. 83-89, 2017.
• [10] B. Bulca, K. Arslan, B. Bayram, and G. Öztürk, “Spherical product surfaces in , Analele Stiintifice ale Universitatii Ovidius Constanta, vol. 20, no. 1, pp. 41-54, 2012.
• [11] P.M. Do Carmo, “Differential Geometry of Curves and Surfaces”, Englewood Cliffs, NJ, USA: Prentice-Hall, 1976.
• [12] G. Ganchev and V. Milousheva, “General rotational surfaces in the 4-dimensional Minkowski space,” Turkish Journal of Mathematics, vol. 38, pp. 883-895, 2014.
• [13] R.O. Gal and L. Pal, “Some notes on drawing twofolds in 4-dimensional Euclidean Space,” Acta Universitatis Sapientiae, Informatica, vol. 1, no. 2, pp. 125-134, 2009.
• [14] F. Gökçelik, Z. Bozkurt, İ. Gök, F.N. Ekmekçi and Y. Yaylı, “Parallel transport frame in 4-dimensional Euclidean space ,” Caspian J. of Math. Sci., vol. 3, pp. 91-103, 2014.
• [15] E. İyigün, K. Arslan, G. Öztürk, “A characterization of Chen surfaces in ,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 31, pp. 209-215, 2008.
• [16] M.K. Karacan and B. Bükçü, “On natural curvatures of Bishop frame,” Journal of Vectorial Relativity, vol. 5, pp. 34-41, 2010.
• [17] İ. Kişi and G. Öztürk, “A new approach to canal surface with parallel transport frame,” International Journal of Geometric Methods in Modern Physics, vol. 14, no. 2, pp. 1-16, 2017.
• [18] T. Maekawa, N.M. Patrikalakis, T. Sakkalis and G. Yu, “Analysis and applications of pipe surfaces,” Computer-Aided Geometric Design, vol. 15, pp. 437-458, 1998.
• [19] G. Öztürk, B. Bulca, B. (Kılıç) Bayram, K. Arslan, “Meridian surfaces of Weingarten type in 4-dimensional Euclidean space ,” Konuralp Journal of Mathematics, vol. 4, no. 1, pp. 239-245, 2016.
• [20] S.J. Ro and D.W. Yoon, “Tubes of Weingarten types in a Euclidean 3-Space,” Journal of the Chungcheong Mathematical Society, vol. 22, pp. 359-366, 2009.
• [21] U. Shani and D.H. Ballard, “Splines as embeddings for generalized cylinders,” Computer Vision Graphics and Image Processing, vol. 27, pp. 129-156, 1984.
• [22] C.K. Shene, “Blending two cones with Dupin cyclids,” Computer-Aided Geometric Design, vol. 15, pp. 643-673, 1998.
• [23] L. Wang, C.L. Ming, and D. Blackmore, “Generating sweep solids for NC verification using the SEDE method,” Proceedings of the Fourth Symposium on Solid Modeling and Applications; 14-16 May 1995; Atlanta. Georgian: pp. 364-375.
• [24] Z. Xu, R. Feng, and J.G. Sun, “Analytic and algebraic properties of canal surfaces,” Journal of Computational and Applied Mathematics,” vol. 195, pp. 220-228, 2006.
• [25] Y.C. Wong, “Contributions to the theory of surfaces in a 4-space of constant curvature,” Trans. Amer. Math. Soc., vol. 59, no. 3, pp. 467-507, 1946.