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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 17 Issue: 1

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

Muhittin Evren Aydın(Fırat Üniversitesi)0000-0001-9337-8165
Lopez Rafael(Universidad de Granada)0000-0003-3108-7009
Sayfa
—
Yayın Tarihi
2024-04-23
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Using this parametrization, we find new examples of rotational minimal surfaces and rotational surfaces with zero Gaussian curvature.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we give a new approach to the rotational minimal surfaces in $4$-dimensional Euclidean space $\mathbb{R}^4$.
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Temel Bulgular & Veri:One type of these surfaces is obtained by the composition of two families of rotations in orthogonal planes.
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Sonuç & Katkı:Using this parametrization, we find new examples of rotational minimal surfaces and rotational surfaces with zero Gaussian curvature.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rotational surface · minimal surface · Gauss curvature

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.

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Bu Makaleye Atıf Yap

Aydın, M. E., Rafael, L. (2024). Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples. International Electronic Journal of Geometry, Volume: 17 Issue: 1. https://doi.org/10.36890/iejg.1430210

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Kaynakça (8)

  1. Arslan, K., Bayram, B.K., Bulca, B., Öztürk, G.: Generalized rotation surfaces in E4. Results Math., 61, 315-327 (2012).
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  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).