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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

Bour's theorem on the Gauss map in 3-Euclidean space

Yusuf YAYLI
H. Hilmi HACISALİHOĞLU
Erhan GÜLER
Sayfa
515–525
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, Bour’s theorem on the Gauss map, and some special examples are given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper some relations are established between the Laplace- Beltrami operator and the curvatures of helicoidal surfaces in 3- Euclidean space.
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Temel Bulgular & Veri:In this paper some relations are established between the Laplace- Beltrami operator and the curvatures of helicoidal surfaces in 3- Euclidean space.
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Sonuç & Katkı:In addition, Bour’s theorem on the Gauss map, and some special examples are given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper some relations are established between the Laplace- Beltrami operator and the curvatures of helicoidal surfaces in 3- Euclidean space. In addition, Bour’s theorem on the Gauss map, and some special examples are given.

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Bu Makaleye Atıf Yap

YAYLI, Y., HACISALİHOĞLU, H. H., GÜLER, E. (2022). Bour's theorem on the Gauss map in 3-Euclidean space. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 515–525. https://ajindex.com/articles/530641

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Kaynakça (8)

  1. Beneki, Chr.C., Kaimakamis, G. and Papantoniou, B. J. Helicoidal surfaces in three dimensional Minkowski space, J. Math. Anlys. Appl. 275, 586-614, 2002
  2. Bour, E. Memoire sur le deformation de surfaces, Journal de l’ˆEcole Polytechnique,XXXIX Cahier, 1–148, 1862
  3. Do Carmo, M.P. and Dajczer, M. Helicoidal surfaces with constant mean curvature, Tohoku Math. J. 34, 425–435, 1982
  4. Güler, E. Helicoidal surfaces in three dimensional Minkowski space (M.Sc. Thesis, Gazi University, Ankara, 2005)
  5. Güler, E. Bour’s theorem and lightlike profile curve, Yokohama Math. J. 54 (1), 55–77, 2007
  6. Ikawa, T. Bour’s theorem and Gauss map, Yokohama Math. J. 48, 173–180, 2000
  7. Kühnel W. Differential Geometry Curves-Surfaces-Manifolds (AMS, 2nd edition, USA,2006)
  8. O’Neill, B. Elementary Differential Geometry (Academic Press, New York, 1966).