[1] Wang Xiaoliu, Chao Xiaoli,. Constant angle surfaces constructed on curves [J]. Journal of Southeast University (English Edition), 2013, 29 (4): 470-472. [doi:10.3969/j.issn.1003-7985.2013.04.022]

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Constant angle surfaces constructed on curves()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

29

Issue:

2013 4

Page:

470-472

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2013-12-20

Info

Title:

Constant angle surfaces constructed on curves

Author(s):

Wang Xiaoliu;  Chao Xiaoli

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

ruled surface;  constant angle surface;  tangent surface;  normal surface;  binormal surface

PACS:

O186.1

DOI:

10.3969/j.issn.1003-7985.2013.04.022

Abstract:

The Frenet-Serret formula is used to characterize the constant angle ruled surfaces in R³. When the surfaces are the tangent developmental and normal surfaces, that is, r(s, v)=σ(s)+v(cosα(s)·t(s)+sinα(s)·n(s)), it is shown that each of these surfaces is locally isometric to a piece of a plane or a certain special surface. When the surfaces are normal and binormal surfaces, that is, r(s, v)=σ(s)+v(cosα(s)·n(s)+sinα(s)·b(s)), it is shown that each of these surfaces is locally isometric to a piece of a plane or a cylindrical surface.

References:

[1] Dillen F, Fastenakels J, van der Veken J, et al. Constant angle surfaces in S²×R [J]. Monatshefte für Mathematik, 2007, 152(2): 89-96.
[2] Dillen F, Munteanu M I. Surfaces in H⁺×R[C]//Proceedings of the Conference Pure and Applied Differential Geometry. Brussels, Belgium, 2007: 185-193.
[3] Dillen F, Munteanu M I. Constant angle surfaces in H²×R [J]. Bull Braz Math Soc, 2009, 40(1): 85-97.
[4] Munteanu M I, Nistor A I. A new approach on constant angle surfaces in E³ [J]. Turkish J Math, 2009, 33(2): 169-178.
[5] López R, Munteanu M I. Constant angle surfaces in Minkowski space [J]. Bull Belg Math Soc Simon Stevin, 2011, 18(2): 271-286.
[6] Munteanu M I. From golden spirals to constant slope surfaces [J]. Journal of Mathematical Physics, 2010, 51(7): 073507.
[7] Di Scala A J, Ruiz-Hernández G. Helix submanifolds of euclidean spaces [J]. Monatshefte für Mathematik, 2009, 157(3): 205-215.
[8] Nistor A I. Certain constant angle surfaces constructed on curves [J]. Int Electron J Geom, 2011, 4(1): 79-87.

Memo

Memo:

Biography: Wang Xiaoliu(1981—), male, doctor, lecturer, xlwang.seu@gmail.com.
Foundation items: The National Natural Science Foundation of China(No.10971029, 11101078, 11171064), the Natural Science Foundation of Jiangsu Province(No.BK2011583).
Citation: Wang Xiaoliu, Chao Xiaoli. Constant angle surfaces constructed on curves[J].Journal of Southeast University(English Edition), 2013, 29(4):470-472.[doi:10.3969/j.issn.1003-7985.2013.04.022]

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