Research Article
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Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples

Year 2024, Volume: 17 Issue: 1, 97 - 105, 23.04.2024

Muhittin Evren Aydın Lopez Rafael

https://doi.org/10.36890/iejg.1430210

Abstract

In this paper, we give a new approach to the rotational minimal surfaces in $4$-dimensional Euclidean space $\mathbb{R}^4$. One type of these surfaces is obtained by the composition of two families of rotations in orthogonal planes. For these surfaces, we give a new parameterization. Using this parametrization, we find new examples of rotational minimal surfaces and rotational surfaces with zero Gaussian curvature.

Keywords

Rotational surface minimal surface Gauss curvature

References

  • [1] Arslan, K., Bayram, B.K., Bulca, B., Öztürk, G.: Generalized rotation surfaces in E4. Results Math., 61, 315-327 (2012).
  • [2] Cole, F. N.: On rotations in space of four dimensions. Amer. J. Math. 12, 191–210 (1890).
  • [3] Dursun, U. Turgay, N.C.: Minimal and pseudo-umbilical rotational surfaces in Euclidean space E4. Mediterr. J. Math. 10, 497–506 (2013).
  • [4] Ganchev, G., Milousheva, V.: General rotational surfaces in the four-dimensional Minkowski space. Turk. J. Math. 38 (5), 883-895 (2014).
  • [5] Lee, H.: Minimal surfaces in R4 foliated by conic sections and parabolic rotations of holomorphic null curves in C4. J. Korean Math. Soc. 57, 1–19 (2020).
  • [6] Lee, H.: Minimal surface system in Euclidean four-space. J. Korean Math. Soc. 60, 71–90 (2023).
  • [7] Moore, C.: Surfaces of rotations in a space of four dimensions. Ann. Math. 21 (2), 81–93 (1919).
  • [8] Vranceanu, G.: Surfaces de rotation dans E4. Rev. Roumaine Math. Pures Appl. 22 (6), 857–862 (1977).

Year 2024, Volume: 17 Issue: 1, 97 - 105, 23.04.2024

Muhittin Evren Aydın Lopez Rafael

https://doi.org/10.36890/iejg.1430210

Abstract

References

  • [1] Arslan, K., Bayram, B.K., Bulca, B., Öztürk, G.: Generalized rotation surfaces in E4. Results Math., 61, 315-327 (2012).
  • [2] Cole, F. N.: On rotations in space of four dimensions. Amer. J. Math. 12, 191–210 (1890).
  • [3] Dursun, U. Turgay, N.C.: Minimal and pseudo-umbilical rotational surfaces in Euclidean space E4. Mediterr. J. Math. 10, 497–506 (2013).
  • [4] Ganchev, G., Milousheva, V.: General rotational surfaces in the four-dimensional Minkowski space. Turk. J. Math. 38 (5), 883-895 (2014).
  • [5] Lee, H.: Minimal surfaces in R4 foliated by conic sections and parabolic rotations of holomorphic null curves in C4. J. Korean Math. Soc. 57, 1–19 (2020).
  • [6] Lee, H.: Minimal surface system in Euclidean four-space. J. Korean Math. Soc. 60, 71–90 (2023).
  • [7] Moore, C.: Surfaces of rotations in a space of four dimensions. Ann. Math. 21 (2), 81–93 (1919).
  • [8] Vranceanu, G.: Surfaces de rotation dans E4. Rev. Roumaine Math. Pures Appl. 22 (6), 857–862 (1977).
There are 8 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Muhittin Evren Aydın 0000-0001-9337-8165

Lopez Rafael 0000-0003-3108-7009

Early Pub Date April 5, 2024
Publication Date April 23, 2024
Submission Date February 1, 2024
Acceptance Date March 10, 2024
Published in Issue Year 2024 Volume: 17 Issue: 1

Cite

APA Aydın, M. E., & Rafael, L. (2024). Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. International Electronic Journal of Geometry, 17(1), 97-105. https://doi.org/10.36890/iejg.1430210
AMA Aydın ME, Rafael L. Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. Int. Electron. J. Geom. April 2024;17(1):97-105. doi:10.36890/iejg.1430210
Chicago Aydın, Muhittin Evren, and Lopez Rafael. “Rotational Surfaces in $\mathbb R^4$ With New Approaches and Examples”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 97-105. https://doi.org/10.36890/iejg.1430210.
EndNote Aydın ME, Rafael L (April 1, 2024) Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. International Electronic Journal of Geometry 17 1 97–105.
IEEE M. E. Aydın and L. Rafael, “Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 97–105, 2024, doi: 10.36890/iejg.1430210.
ISNAD Aydın, Muhittin Evren - Rafael, Lopez. “Rotational Surfaces in $\mathbb R^4$ With New Approaches and Examples”. International Electronic Journal of Geometry 17/1 (April 2024), 97-105. https://doi.org/10.36890/iejg.1430210.
JAMA Aydın ME, Rafael L. Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. Int. Electron. J. Geom. 2024;17:97–105.
MLA Aydın, Muhittin Evren and Lopez Rafael. “Rotational Surfaces in $\mathbb R^4$ With New Approaches and Examples”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 97-105, doi:10.36890/iejg.1430210.
Vancouver Aydın ME, Rafael L. Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. Int. Electron. J. Geom. 2024;17(1):97-105.
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