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

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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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[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).