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Original Articles
Intrinsic Equations of Some Special Curves in Euclidean 3-Space
Ahmad Tawfik Aliatali71@yahoo.comFaculty of ScienceAl-Azhar UniversityMathematics Department, Nasr City, Cairo, 11884, EgyptView full profile →
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- Received:
- 19 May 2012
- Accepted:
- 20 Jul 2012
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2012.10698615
- Pages:
- 129–138
Abstract
In this paper, we obtain the intrinsic equations of some special curves in Euclidean 3-space characterized by det = 0, where rundefined < rundefined,r1 ∈ {1, 2, 3}, r2 ∈ {2, 3, 4} and r3 ∈ {3, 4, 5}.
References
- Ali, A.T.2010 . Position vectors of spacelike general helices in Minkowski 3-space . , 73 : 1118 – 1126 .
- Ali, A.T. and Turgut, M.2010 . Position vector of a time-like slant helix in Minkowski 3-space . , 365 : 559 – 569 .
- Ali, A.T.2010 . Position vectors of general helices in Euclidean 3-space . , 3 ( 2 ) : 198 – 205 .
- Ali, A.T.2012 . Position vectors of slant helices in Euclidean 3-space . , 20 : 1 – 6 .
- Ali, A.T.2012 . New special curves and their spherical indicatrices . , 1 ( 2 ) : 28 – 38 .
- Barros, M.1997 . General helices and a theorem of Lancret . , 125 : 1503 – 1509 .
- Do Carmo, M.P.1976 . , Englewood Cliffs: Prentice Hall .
- Izumiya, S. and Takeuchi, N.2004 . New special curves and developable surfaces . , 28 : 531 – 537 .
- Izumiya, S. and Takeuchi, N.2002 . Generic properties of helices and Bertrand geometry . , 74 : 97 – 109 .
- Kula, L. and Yayli, Y.2005 . On slant helix and its spherical indicatrix . , 169 : 600 – 607 .
- Kula, L., Ekmekci, N., Yayli, Y. and Ilarslan, K.2010 . Characterizations of slant helices in Euclidean 3-space . , 34 : 261 – 274 .
- Monterde, J.2007 . Curves with constant curvature ratios . , 13 : 177 – 186 .
- Monterde, J.2009 . Salkowski curves revisted: A family of curves with constant curvature and nonconstant torsion . , 26 : 271 – 278 .
- Salkowski, E.1909 . Zur transformation von raumkurven . , 66 : 517 – 557 .
- Struik, D.J.1961 . , Reading: Addison-Wesley .
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