CHARACTERIZATIONS OF SOME ASSOCIATED AND SPECIAL CURVES TO TYPE-2 BISHOP FRAME IN E^3

Abstract

In this paper, we investigate associated curves according to type-2 Bishop frame in E^3. In addition, necessary and sufficient conditions for a curve to be a regular one are studied to the mentioned frame. Finally we give characterization of the are length of spherical indicatrice and inclined curve using harmonic curvature.

Keywords

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References

1. J. F. Burke, Bertrand curves associated with a pair of curves, Mathematics Magazine. 34(1), 60-62, 1960.
2. R. Ghedami, Y. Yaylı, A new characterization for inclined curves by the help of spherical representations according to Bishop frame, Intl Jour Pure Appl Math, 74(4) 455-463, 2012 .
3. S. Yılmaz, M. Turgut, A new version of Bishop frame and an application to spherical images. J Math Anal Appl 371:764-776, 2010.
4. M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Saddle River, 1976.
5. B. O’Neill, Elementary differential geometry, Academic Press, New York, 1966.
6. S. Yılmaz, Spherical indicators of curves and characterizations of some special curves in four dimensional Lorentzian space L^4 , PhD Dissertation, Dokuz Eylül University, 2001.
7. G. Canuto, Associated curves and Plücker formulas in Grassmannians , Inventiones Mathematicae , 53 (1) , 77-90, 1979.
8. J.H. Choi, Y.H. Kim, Associated curves of a Frenet curve and their applications. Appl Math Comput, 218: 9116–9124, 2012.

9. S.Yılmaz , Position vectors of some special space-like curves according to Bishop frame in Minkowski space E_1^3 , Sci Magna , 5(1), 48-50, 2010.
10. T. Körpınar, M. Sarıaydın and E. Turhan, Associated curves according to Bishop frame in Euclideam space , AMO-Advanced and Optimization, 15(3), 713-717, 2013.
11. E. Özyılmaz, Classical differential geometry of curves according to type-2 Bishop trihedra, Math Comput Appl, 16(4), 858-867, 2011.