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2010 | 8 | 3 | 430-436
Tytuł artykułu

Polynomial translation surfaces of Weingarten types in Euclidean 3-space

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
3
Strony
430-436
Opis fizyczny
Daty
wydano
2010-06-01
online
2010-05-30
Twórcy
autor
Bibliografia
  • [1] Baikoussis C., Koufogiorgos Th., On the inner curvature of the second fundamental form of helicoidal surfaces, Arch. Math., 1997, 68, 169–176 http://dx.doi.org/10.1007/s000130050046
  • [2] Blair D.E., Koufogiorgos Th., Ruled surfaces with vanishing second Gaussian curvature, Monatsh. Math., 1992, 113, 177–181 http://dx.doi.org/10.1007/BF01641765
  • [3] Dillen F., Goemans W., Van de Woestyne I., Translation surfaces of Weingarten type in 3-space, Bull. Transilvania Univ. Brasov (Ser. III), 2008, 50, 109–122
  • [4] Dillen F., Kühnel W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 1999, 98, 307–320 http://dx.doi.org/10.1007/s002290050142
  • [5] Dillen F., Sodsiri W., Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom., 2005, 83, 10–21 http://dx.doi.org/10.1007/s00022-005-0002-4
  • [6] Goemans W., Van de Woestyne I., Translation surfaces with the second fundamental form with vanishing Gaussian curvature in Euclidean and Minkowski 3-space, Proceeding PADGE, 2007
  • [7] Kim Y.H., Yoon D.W., Classification of ruled surfaces in Minkowski 3-spaces, J. Geom. Phys., 2004, 49, 89–100 http://dx.doi.org/10.1016/S0393-0440(03)00084-6
  • [8] Koufogiorgos Th., Hasanis T., A characteristic property of the sphere, Proc. Amer. Math. Soc., 1977, 67, 303–305 http://dx.doi.org/10.2307/2041291
  • [9] Koutroufiotis D., Two characteristic properties of the sphere, Proc. Amer. Math. Soc., 1974, 44, 176–178 http://dx.doi.org/10.2307/2039251
  • [10] Kühnel W., Ruled W-surfaces, Arch. Math., 1994, 62, 475–480 http://dx.doi.org/10.1007/BF01196440
  • [11] López R., Special Weingarten surfaces foliated by circles, Monatsh. Math., 2008, 154(4), 289–302 http://dx.doi.org/10.1007/s00605-008-0557-x
  • [12] Munteanu M.I., Nistor A.I., Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space, In: Differential Geometry, Proceedings of the VIII International Colloquium, Santiago de Compostela, Spain, World Scientific, Hackensack, 2009, 316–320 http://dx.doi.org/10.1142/9789814261173_0034
  • [13] Munteanu M.I., Nistor A.I., On the geometry of the second fundamental form of translation surface in \( \mathbb{E}^3 \) , Houston J. Math., 2010, (in print), preprint available at http://arxiv.org/abs/0812.3166
  • [14] Yoon D.W., Some properties of the helicoid as ruled surfaces, JP Jour. Geom. Topology, 2002, 2, 141–147
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0034-3
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