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AN APPLICATION OF FACTORABLE SURFACES IN EUCLIDEAN 4-SPACE E4

Year 2019, Volume: 9 Issue: 1, 121 - 127, 01.03.2019

Abstract

In the present paper, we consider the factorable surfaces in Euclidean 4-space E4. We characterize such surfaces in terms of their Gaussian curvature, Gaussian torsion and mean curvature. Further, we classify at, semiumbilical and minimal factorable surfaces in E4.

References

  • Arslan, K., Bayram, B. K., Bulca, B., Kim, Y.H., Murathan, C., ¨Ozt¨urk, G., (2011), Vranceanu Surface in E4with Pointwise 1-Type Gauss Map, Indian J. Pure Appl. Math., 42(1), pp. 41-51.
  • Bulca, B., Arslan, K., (2013), Surfaces Given with the Monge Patch in E4, Journal of Mathematical Physics, Analysis, Geometry, 9(4), pp. 435-447.
  • Bulca, B., Arslan, K., Bayram, B.K., ¨Ozt¨urk, G., (2012), Spherical Product Surface in E4, Ann. St. Univ. Ovidius Constanta, 20(1), pp. 41-54.
  • B¨uy¨ukk¨ut¨uk, S., ¨Ozt¨urk, G. (2018), A Characterization of Factorable Surfaces in Euclidean 4−Space E, Koc. J. Sci. Eng., 1(1), pp. 15-20.
  • Chen, B. Y., (1973), Geometry of Submanifolds, Dekker, New York.
  • Gutierrez Nunez, J. M., Romero Fuster, M. C., Sanchez-Bringas F., (2008), Codazzi Fields on Surfaces Immersed in Euclidean 4−spaces, Osaka J. Math., 45, pp. 877-894.
  • Meng, H., Liu, H., (2009), Factorable Surfaces in 3−Minkowski Space, Bull. Korean Math. Soc., 46(1), pp. 155-169.
  • Woestyne, I. V., (1993), A new characterization of helicoids, Geometry and topology of submanifolds, World Sci. Publ., River Edge, NJ., pp. 267-273.
  • Yu, Y., Liu, H., (2007), The factorable minimal surfaces, Proceedings of The Eleventh International Workshop on Diff. Geom., 11, pp. 33-39.
Year 2019, Volume: 9 Issue: 1, 121 - 127, 01.03.2019

Abstract

References

  • Arslan, K., Bayram, B. K., Bulca, B., Kim, Y.H., Murathan, C., ¨Ozt¨urk, G., (2011), Vranceanu Surface in E4with Pointwise 1-Type Gauss Map, Indian J. Pure Appl. Math., 42(1), pp. 41-51.
  • Bulca, B., Arslan, K., (2013), Surfaces Given with the Monge Patch in E4, Journal of Mathematical Physics, Analysis, Geometry, 9(4), pp. 435-447.
  • Bulca, B., Arslan, K., Bayram, B.K., ¨Ozt¨urk, G., (2012), Spherical Product Surface in E4, Ann. St. Univ. Ovidius Constanta, 20(1), pp. 41-54.
  • B¨uy¨ukk¨ut¨uk, S., ¨Ozt¨urk, G. (2018), A Characterization of Factorable Surfaces in Euclidean 4−Space E, Koc. J. Sci. Eng., 1(1), pp. 15-20.
  • Chen, B. Y., (1973), Geometry of Submanifolds, Dekker, New York.
  • Gutierrez Nunez, J. M., Romero Fuster, M. C., Sanchez-Bringas F., (2008), Codazzi Fields on Surfaces Immersed in Euclidean 4−spaces, Osaka J. Math., 45, pp. 877-894.
  • Meng, H., Liu, H., (2009), Factorable Surfaces in 3−Minkowski Space, Bull. Korean Math. Soc., 46(1), pp. 155-169.
  • Woestyne, I. V., (1993), A new characterization of helicoids, Geometry and topology of submanifolds, World Sci. Publ., River Edge, NJ., pp. 267-273.
  • Yu, Y., Liu, H., (2007), The factorable minimal surfaces, Proceedings of The Eleventh International Workshop on Diff. Geom., 11, pp. 33-39.
There are 9 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

S. Büyükkütük This is me

G. Öztürk This is me

Publication Date March 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

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