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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 4

Constructions of helicoidal surfaces by using curvature functions in isotropic space

Dae Won Yoon0000-0001-8620-0676
Jae Won Lee0000-0001-8562-0767
Chul Woo Lee0000-0003-0223-2318
Sayfa
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Yayın Tarihi
2019-08-08
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions.
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Temel Bulgular & Veri:In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions.
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Sonuç & Katkı:Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Isotropic space · helicoidal surface · mean curvature

Abstract

In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions. Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.

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Bu Makaleye Atıf Yap

Yoon, D. W., Lee, J. W., Lee, C. W. (2019). Constructions of helicoidal surfaces by using curvature functions in isotropic space. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 4. https://ajindex.com/articles/1402754

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Kaynakça (12)

  1. M.E. Aydin, Classification results on surfaces in the isotropic 3-space, AKU J. Sci. Eng. 16, 239-246, 2016.
  2. C. Baikoussis and T. Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature, J. Geom. 63, 25-29, 1988.
  3. Chr.C. Beneki, G. Kaimakamis and B.J. Papantonios, Helicoidal surfaces in threedimensional Minkowski space, J. Math. Anal. Appl. 275, 586-614, 2002.
  4. R. Caddeo, P. Piu and A. Ratto, Rotation surfaces in $H_3$ with constant Gauss curvature, Bollettino U.M.I. 7, 341-357, 1996.
  5. C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pures Appl. Series 1 6, 309-320, 1841.
  6. M.P. do Carmo and M. Dajczer, Helicoidal surfaces with constant mean curvature, Tôhoku Math. J. 34 (3), 425-435, 1982.
  7. A. Gray, Modern differential geometry of curves and surfaces, CRC Press 1993.
  8. J.-I. Hano and K. Nomizu, Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space, Tôhoku Math. J. 36, 427-437, 1984.
  9. F. Ji and Z.H. Hou, Helicoidal surfaces under the cubic screw motion in Minkowski 3-space, J. Math. Anal. Appl. 318, 634-647, 2006.
  10. H. Pottmann, P. Grohs and N.J. Mitra, Laguerre minimal surfaces, isotropic geometry and linear elasticity, Adv. Comput. Math. 31, 391-419, 2009.
  11. Ž.M. Šipuš, Translation surfaces of constant curvatures in a simply isotropic space, Period. Math. Hungar. 68, 160-175, 2014.
  12. D.W. Yoon, D.-S. Kim, Y.H. Kim and J.W. Lee, Helicoidal surfaces with prescribed curvature in $Nil_3$, International J. Math. 24, 1350107 (11 pages), 2013.