Previous |  Up |  Next

# Article

Full entry | PDF   (0.7 MB)
Keywords:
Weingarten surfaces; Lorentzian motion; ruled surfaces
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.
References:
[1] Abdel-All, N. H., Abdel-Baky, R. A., Hamdon, F. M.: Ruled surfaces with timelike rulings. Appl. Math. Math. Comput. 147 (2004), 241–253. DOI 10.1016/S0096-3003(02)00664-1 | MR 2008252
[2] Blair, D. E., Koufogioros, Th.: Ruled surfaces with vanishing second Gaussian curvature. Monatsh. Math. 113 (1992), 177–181. DOI 10.1007/BF01641765 | MR 1163298
[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
[4] Dillen, F., Kuhnel, W.: Ruled Weingarten surfaces in Minkowski 3-space. Manuscripta Math. 98 (1999), 307–320. DOI 10.1007/s002290050142 | MR 1717535
[5] Dillen, F., Sodsiri, W.: Ruled surfaces of Weingarten type in Minkowski 3-space. J. Geom. 83 (2005), 10–21. DOI 10.1007/s00022-005-0002-4 | MR 2193223 | Zbl 1110.53013
[6] Ho Kim, Y., Won Yoon, D.: Classification of ruled surfaces in Minkowski 3-space. J. Geom. Phys. 49 (2004), 89–100. DOI 10.1016/S0393-0440(03)00084-6 | MR 2077246
[7] Koufogioros, Th., Hasanis, T.: A characteristic property of the sphere. Proc. Amer. Math. Soc. 44 (1977), 303–305. DOI 10.1090/S0002-9939-1977-0487927-7 | MR 0487927
[8] Kuhnel, W.: On the inner curvature of the second fundamental form. Proc. 3rd. Congress Geometry, Thessaloniki (1991), 248–253. MR 1175436
[9] Kuhnel, W.: Ruled W-surfaces. Arch. Math. (Basel) 62 (1994), 475–480. DOI 10.1007/BF01196440 | MR 1274756
[10] Mc-Nertney, L. V.: One-parameter families of surfaces with constant curvature in Lorentz 3-space. Ph.D. thesis, Brown University, 1980.
[11] O’Neil, B.: Semi-Riemannian Geometry. Academic Press, New York-London, 1983. MR 0719023
[12] Sodsiri, W.: Ruled linear Weingarten surfaces in Minkowski 3-space. Soochow J. Math. 29 (2003), 435–443. MR 2021543

Partner of