Polynomial translation surfaces of Weingarten types in Euclidean 3-space

Dae Yoon

Open Mathematics (2010)

  • Volume: 8, Issue: 3, page 430-436
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dae Yoon. "Polynomial translation surfaces of Weingarten types in Euclidean 3-space." Open Mathematics 8.3 (2010): 430-436. <http://eudml.org/doc/269663>.

@article{DaeYoon2010,
abstract = {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.},
author = {Dae Yoon},
journal = {Open Mathematics},
keywords = {Translation surface; Jacobi equation; Gaussian curvature; Mean curvature; Second Gaussian curvature; translation surface; mean curvature; second Gaussian curvature},
language = {eng},
number = {3},
pages = {430-436},
title = {Polynomial translation surfaces of Weingarten types in Euclidean 3-space},
url = {http://eudml.org/doc/269663},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Dae Yoon
TI - Polynomial translation surfaces of Weingarten types in Euclidean 3-space
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 430
EP - 436
AB - 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.
LA - eng
KW - Translation surface; Jacobi equation; Gaussian curvature; Mean curvature; Second Gaussian curvature; translation surface; mean curvature; second Gaussian curvature
UR - http://eudml.org/doc/269663
ER -

References

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  10. [10] Kühnel W., Ruled W-surfaces, Arch. Math., 1994, 62, 475–480 http://dx.doi.org/10.1007/BF01196440 Zbl0794.53008
  11. [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 Zbl1169.53005
  12. [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 Zbl1179.53005
  13. [13] Munteanu M.I., Nistor A.I., On the geometry of the second fundamental form of translation surface in 𝔼 3 , Houston J. Math., 2010, (in print), preprint available at http://arxiv.org/abs/0812.3166 
  14. [14] Yoon D.W., Some properties of the helicoid as ruled surfaces, JP Jour. Geom. Topology, 2002, 2, 141–147 Zbl1038.53005

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