Other Articles by Authors

Hassan Al-Zoubi

Authors and WSEAS

Hassan Al-Zoubi

WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

Tubes of Finite II-Type in the Euclidean 3-Space

AUTHORS: Hassan Al-Zoubi

Download as PDF

ABSTRACT: In this paper, we consider surfaces in the 3-dimensional Euclidean space E3 which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form. We present an important family of surfaces, namely, tubes in E3 . We show that tubes are of infinite II-type.

KEYWORDS: Surfaces in the Euclidean 3-space, Surfaces of finite Chen-type, Beltrami operator


[1] C. Baikoussis, L. Verstraelen, The Chen-Type of the Spiral Surfaces, Results. Math., 28 (1995), 214-223.

[2] W. Blaschke, und K. Leichtwiss, Elementare Differentialgeometrie. Springer, Berlin 1973.

[3] B.-Y. Chen, Total mean curvature and submanifolds of finite type, 2 nd edition. World Scientific Publisher, 2015.

[4] B.-Y. Chen, Surfaces of finite type in Euclidean 3-space, Bull.Soc. Math. Belg., 39 (1987), 243- 254.

[5] B.-Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math., 17 (1991), 169-188.

[6] B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math., 22 (1996), 117-337.

[7] B.-Y. Chen, F. Dillen, L. Verstraelen, L. Vrancken, Ruled surfaces of finite type, Bull. Austral. Math. Soc., 42 (1990), 447-453.

[8] B.-Y. Chen, F. Dillen, Quadrics of finite type, J. of Geom., 38 (1990), 16-22.

[9] B.-Y. Chen, S. Ishikawa, On classification of some surfaces of revolution of finite type. Tsukuba J. Math. 17 (1993), 287-298.

[10] JF. Defever, R. Deszcz and L. Verstraelen, The compact cyclides of Dupin and a conjecture of B.-Y. Chen. J. Geom. 46 (1993), 33-38.

[11] F. Dillen, J. Pas, L. Verstraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J., 13 (1990), 10-21.

[12] W. Haack, Elementtare Differetialgeometrie, Basel und Stuttgart, Berkhauser 1955. ¨

[13] O. Garay, An extension of Takahashi’s theorem, Geometriae dedicate, 34 (1990), 105-112.

[14] Y. H. Kim, C. W. Lee, D. W. Yoon, On the Gauss map of surfaces of revolution without parabolic points, Bull. Korean Math. Soc., 46 (2009), 11411149

[15] J. S. Ro, D. W. Yoon. Tubes of Weingarten types inEuclidean 3-space, J. Cungcheong Math. Soc., 22 (2009), 359-366.

[16] S. Stamatakis, H. Al-Zoubi, On surfaces of finite Chen-type, Results. Math., 43 (2003), 181-190.

[17] S. Stamatakis, H. Al-Zoubi, Surfaces of revolution satisfying 4IIIx = Ax, Journal for Geometry and Graphics, 14 (2010), 181-186.

[18] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380-385.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #1, pp. 1-5

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board


The editorial board is accepting papers.

WSEAS Main Site