| Title:
|
Ruled W-surfaces in Minkowski 3-space $\Re _{1}^{3}$ (English) |
| Author:
|
Abdel-Baky, R. A. |
| Author:
|
Abd-Ellah, H. N. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
251-263 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set $\lbrace K,\ K_{II},\ H,\ H_{II}\rbrace $, where $(K, H)$ and $(K_{II}, H_{II})$ are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted. (English) |
| Keyword:
|
Weingarten surfaces |
| Keyword:
|
Lorentzian motion |
| Keyword:
|
ruled surfaces |
| MSC:
|
53A10 |
| MSC:
|
53A35 |
| MSC:
|
53B30 |
| idZBL:
|
Zbl 1212.53007 |
| idMR:
|
MR2493422 |
| . |
| Date available:
|
2009-01-29T09:15:15Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119765 |
| . |
| Reference:
|
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| Reference:
|
[2] Blair, D. E., Koufogioros, Th.: Ruled surfaces with vanishing second Gaussian curvature.Monatsh. Math. 113 (1992), 177–181. MR 1163298, 10.1007/BF01641765 |
| Reference:
|
[3] de Woestyne I., Van: Geometry and Topology of Submanifolds II.ch. Minimal surfaces of the 3-dimensional Minkowski space, pp. 344–369, World Scientific, Singapore, 1990. MR 1068747 |
| Reference:
|
[4] Dillen, F., Kuhnel, W.: Ruled Weingarten surfaces in Minkowski 3-space.Manuscripta Math. 98 (1999), 307–320. MR 1717535, 10.1007/s002290050142 |
| Reference:
|
[5] Dillen, F., Sodsiri, W.: Ruled surfaces of Weingarten type in Minkowski 3-space.J. Geom. 83 (2005), 10–21. Zbl 1110.53013, MR 2193223, 10.1007/s00022-005-0002-4 |
| Reference:
|
[6] Ho Kim, Y., Won Yoon, D.: Classification of ruled surfaces in Minkowski 3-space.J. Geom. Phys. 49 (2004), 89–100. MR 2077246, 10.1016/S0393-0440(03)00084-6 |
| Reference:
|
[7] Koufogioros, Th., Hasanis, T.: A characteristic property of the sphere.Proc. Amer. Math. Soc. 44 (1977), 303–305. MR 0487927, 10.1090/S0002-9939-1977-0487927-7 |
| Reference:
|
[8] Kuhnel, W.: On the inner curvature of the second fundamental form.Proc. 3rd. Congress Geometry, Thessaloniki (1991), 248–253. MR 1175436 |
| Reference:
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[9] Kuhnel, W.: Ruled W-surfaces.Arch. Math. (Basel) 62 (1994), 475–480. MR 1274756, 10.1007/BF01196440 |
| Reference:
|
[10] Mc-Nertney, L. V.: One-parameter families of surfaces with constant curvature in Lorentz 3-space.Ph.D. thesis, Brown University, 1980. |
| Reference:
|
[11] O’Neil, B.: Semi-Riemannian Geometry.Academic Press, New York-London, 1983. MR 0719023 |
| Reference:
|
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| . |
