Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space

Yıl 2019, Cilt: 12 Sayı: 2, 202 - 209, 03.10.2019

İlim Kişi , Günay Öztürk

https://doi.org/10.36890/iejg.628083

Cited By: 4

Öz

Anahtar Kelimeler

tubular surface, Gauss map, pointwise 1-type

Kaynakça

• [1] Arslan, K., Bayram, B. K., Bulca, B., Kim, Y. H., Murathan, C. and Öztürk, G., Rotational embeddings in E4 with pointwise 1-type Gauss map. Turk. J. Math. 35 (2011), 493-499.
• [2] Arslan, K., Bulca, B. and Milousheva, V., Meridian surfaces in E4 with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 51 (2014), 911-922.
• [3] Arslan, K. and Milousheva, V., Meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space. Taiwanese J. Math. 20 (2016), 311-332.
• [4] Baikoussis, C. and Blair, D. E., On the Gauss map of ruled surfaces. Glasgow Math. J. 34 (1992), 355-359.
• [5] Baikoussis, C., Chen, B. Y. and Verstraelen, L., Ruled surfaces and tubes with finite type Gauss map. Tokyo J. Math. 16 (1993), 341-349.
• [6] Baikoussis, C. and Verstraelen, L., On the Gauss map of helicoidal surfaces. Rend. Sem. Mat. Messina Ser. II 16 (1993), 31-42.
• [7] Bulca, B., A characterization of surfaces in E4. PhD Thessis. 2012.
• [8] Bulca, B., Arslan, K., Bayram, B. and Öztürk, G., Canal surfaces in 4-dimensional Euclidean space. IJOCTA 7 (2017), 83-89. [9] Chen, B. Y., Geometry of Submanifolds. Dekker, New York, 1973.
• [10] Chen, B. Y., Total Mean Curvature and Submanifolds of Finite Type. Series in Pure Mathematics. 1. World Scientific Publishing Co. Singapore, 1984.
• [11] Chen, B. Y., A report on submanifolds of finite type. Soochow J. Math. 22 (1996), 117-337.
• [12] Chen, B. Y., On submanifolds of finite type. Soochow J. Math. 9 (1983), 65-81.
• [13] Chen, B. Y. and Piccinni, P., Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35 (1987), 161-186.
• [14] Chen, B. Y., Choi, M. and Kim, Y. H., Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. 42 (2005), 447-455.
• [15] Choi, M. and Kim, Y. H., Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38 (2001), 753-761.
• [16] Dursun, U., On spacelike rotational surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 52 (2015), 301-312.
• [17] Dursun, U. and Arsan, G. G., Surfaces in the Euclidean space E4 with pointwise 1-type Gauss map. Hacettepe Journal of Mathematics and Statistics 40 (2011), 617-625.
• [18] Farouki, R. T. and Neff, C. A., Analytic properties of plane offset curves. Computer-Aided Geometric Design 7 (1990), 83-99. [19] Farouki, R. T. and Neff, C. A., Algebraic properties of plane offset curves. Computer-Aided Geometric Design 7 (1990), 101-127.
• [20] Gal, R. O. and Pal, L., Some notes on drawing twofolds in 4-dimensional Euclidean space. Acta Univ. Sapientiae, Informatica 1 (2009), 125-134.
• [21] Kim, Y. H. and Yoon, D. W., Ruled surfaces with pointwise 1-type Gauss map. J. Geom. Phys. 34 (2000), 191-205.
• [22] Kim, Y. H. and Yoon, D. W., Classification of rotation surfaces in pseudo-Euclidean space. J. Korean Math. 41 (2004), 379-396.
• [23] Kim, Y. H. and Yoon, D. W., Ruled surfaces with finite type Gauss map in Minkowski spaces. Soochow J. Math. 26 (2000), 85-96.
• [24] Kişi, İ., Öztürk, G. and Arslan, K., A new type of canal surface in Euclidean 4-space E4. Sakarya University Journal of Science 23(5) (2019), 801-809.
• [25] Kişi, İ. and Öztürk, G., A new approach to canal surface with parallel transport frame. Int. J. Geom. Methods Mod. Phys. 14 (2017), 1750026- 1-1750026-16.
• [26] Niang, A., Rotation surfaces with 1-type Gauss map. Bull. Korean Math. Soc. 42 (2005), 23-27. Gauss map of translation surfaces in Minkowski 3-spaces. Taiwanese J. Math. 6 (2002), 389-398.