Weingarten quadric surfaces in a Euclidean 3-space

In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.

Anahtar Kelimeler:

Quadric surface, Weingarten surface, Gaussian curvature, mean curvature

Weingarten quadric surfaces in a Euclidean 3-space

In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.

Keywords:

Quadric surface, Weingarten surface, Gaussian curvature, mean curvature,

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Monatsh. Math. 138, 133-144 (2003).
Kim, Y. H. and Yoon, D. W.: ClassiŞcation of ruled surfaces in Minkowski 3-spaces. J. Geom. Phys. 49, 89-100 (2004).
K¨uhnel, W.: Ruled W-surfaces, Arch. Math. 62, 475-480 (1994).
L´opez, R.: On linear Weingarten surfaces. International J. Math. 19, 439-448 (2008).
L´opez, R.: Special Weingarten surfaces foliated by circles. Monatsh. Math. 154, 289-302 (2008).
L´opez, R.: Parabolic Weingarten surfaces in hyperbolic space. Publ. Math. Debrecen 74, 59-80 (2009).
Munteanu, M. I. and Nistor, A. I.: Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space. arXiv:0809.4745v1 [math.DG] 27 Sep 2008.
Yoon, D. W.: Some properties of the helicoid as ruled surfaces. JP Jour. Geom. Topology 2, 141-147 (2002).
Min Hee KIM, Dae Won YOON Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, South-KOREA e-mail: 1205mh@hanmail.net, dwyoon@gnu.ac.kr