Ruled W-surfaces in Minkowski 3-space $\Re _{1}^{3}$

Abdel-Baky, Rashad A., and Abd-Ellah, H. N.. "Ruled W-surfaces in Minkowski 3-space $\Re _{1}^{3}$." Archivum Mathematicum 044.4 (2008): 251-263. <http://eudml.org/doc/261049>.

@article{Abdel2008,
abstract = {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.},
author = {Abdel-Baky, Rashad A., Abd-Ellah, H. N.},
journal = {Archivum Mathematicum},
keywords = {Weingarten surfaces; Lorentzian motion; ruled surfaces; Weingarten surfaces; Lorentzian motion; ruled surfaces},
language = {eng},
number = {4},
pages = {251-263},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ruled W-surfaces in Minkowski 3-space $\Re _\{1\}^\{3\}$},
url = {http://eudml.org/doc/261049},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Abdel-Baky, Rashad A.
AU - Abd-Ellah, H. N.
TI - Ruled W-surfaces in Minkowski 3-space $\Re _{1}^{3}$
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 4
SP - 251
EP - 263
AB - 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.
LA - eng
KW - Weingarten surfaces; Lorentzian motion; ruled surfaces; Weingarten surfaces; Lorentzian motion; ruled surfaces
UR - http://eudml.org/doc/261049
ER -

References

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Abdel-All, N. H., Abdel-Baky, R. A., Hamdon, F. M., 10.1016/S0096-3003(02)00664-1, Appl. Math. Math. Comput. 147 (2004), 241–253. (2004) MR2008252 DOI10.1016/S0096-3003(02)00664-1
Blair, D. E., Koufogioros, Th., 10.1007/BF01641765, Monatsh. Math. 113 (1992), 177–181. (1992) MR1163298 DOI10.1007/BF01641765
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. (1990) MR1068747
Dillen, F., Kuhnel, W., 10.1007/s002290050142, Manuscripta Math. 98 (1999), 307–320. (1999) MR1717535 DOI10.1007/s002290050142
Dillen, F., Sodsiri, W., 10.1007/s00022-005-0002-4, J. Geom. 83 (2005), 10–21. (2005) Zbl1110.53013 MR2193223 DOI10.1007/s00022-005-0002-4
Ho Kim, Y., Won Yoon, D., 10.1016/S0393-0440(03)00084-6, J. Geom. Phys. 49 (2004), 89–100. (2004) MR2077246 DOI10.1016/S0393-0440(03)00084-6
Koufogioros, Th., Hasanis, T., 10.1090/S0002-9939-1977-0487927-7, Proc. Amer. Math. Soc. 44 (1977), 303–305. (1977) MR0487927 DOI10.1090/S0002-9939-1977-0487927-7
Kuhnel, W., On the inner curvature of the second fundamental form, Proc. 3rd. Congress Geometry, Thessaloniki (1991), 248–253. (1991) MR1175436
Kuhnel, W., 10.1007/BF01196440, Arch. Math. (Basel) 62 (1994), 475–480. (1994) MR1274756 DOI10.1007/BF01196440
Mc-Nertney, L. V., One-parameter families of surfaces with constant curvature in Lorentz 3-space, Ph.D. thesis, Brown University, 1980. (1980)
O’Neil, B., Semi-Riemannian Geometry, Academic Press, New York-London, 1983. (1983) MR0719023
Sodsiri, W., Ruled linear Weingarten surfaces in Minkowski 3-space, Soochow J. Math. 29 (2003), 435–443. (2003) MR2021543

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