Research Article
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Year 2019, , 202 - 209, 03.10.2019
https://doi.org/10.36890/iejg.628083

Abstract

References

  • [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.

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

Year 2019, , 202 - 209, 03.10.2019
https://doi.org/10.36890/iejg.628083

Abstract


References

  • [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.
There are 24 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

İlim Kişi

Günay Öztürk

Publication Date October 3, 2019
Published in Issue Year 2019

Cite

APA Kişi, İ., & Öztürk, G. (2019). Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space. International Electronic Journal of Geometry, 12(2), 202-209. https://doi.org/10.36890/iejg.628083
AMA Kişi İ, Öztürk G. Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space. Int. Electron. J. Geom. October 2019;12(2):202-209. doi:10.36890/iejg.628083
Chicago Kişi, İlim, and Günay Öztürk. “Tubular Surface Having Pointwise 1-Type Gauss Map in Euclidean 4-Space”. International Electronic Journal of Geometry 12, no. 2 (October 2019): 202-9. https://doi.org/10.36890/iejg.628083.
EndNote Kişi İ, Öztürk G (October 1, 2019) Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space. International Electronic Journal of Geometry 12 2 202–209.
IEEE İ. Kişi and G. Öztürk, “Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 202–209, 2019, doi: 10.36890/iejg.628083.
ISNAD Kişi, İlim - Öztürk, Günay. “Tubular Surface Having Pointwise 1-Type Gauss Map in Euclidean 4-Space”. International Electronic Journal of Geometry 12/2 (October 2019), 202-209. https://doi.org/10.36890/iejg.628083.
JAMA Kişi İ, Öztürk G. Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space. Int. Electron. J. Geom. 2019;12:202–209.
MLA Kişi, İlim and Günay Öztürk. “Tubular Surface Having Pointwise 1-Type Gauss Map in Euclidean 4-Space”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 202-9, doi:10.36890/iejg.628083.
Vancouver Kişi İ, Öztürk G. Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space. Int. Electron. J. Geom. 2019;12(2):202-9.