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

Year 2015, Volume: 1 Issue: 1, 66 - 77, 08.01.2016

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.

References

  • J. F. Burke, Bertrand curves associated with a pair of curves, Mathematics Magazine. 34(1), 60-62, 1960.
  • 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 .
  • S. Yılmaz, M. Turgut, A new version of Bishop frame and an application to spherical images. J Math Anal Appl 371:764-776, 2010.
  • M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Saddle River, 1976.
  • B. O’Neill, Elementary differential geometry, Academic Press, New York, 1966.
  • 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.
  • G. Canuto, Associated curves and Plücker formulas in Grassmannians , Inventiones Mathematicae , 53 (1) , 77-90, 1979.
  • J.H. Choi, Y.H. Kim, Associated curves of a Frenet curve and their applications. Appl Math Comput, 218: 9116–9124, 2012.
  • 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.
  • 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.
  • E. Özyılmaz, Classical differential geometry of curves according to type-2 Bishop trihedra, Math Comput Appl, 16(4), 858-867, 2011.

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Year 2015, Volume: 1 Issue: 1, 66 - 77, 08.01.2016

Abstract

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References

  • J. F. Burke, Bertrand curves associated with a pair of curves, Mathematics Magazine. 34(1), 60-62, 1960.
  • 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 .
  • S. Yılmaz, M. Turgut, A new version of Bishop frame and an application to spherical images. J Math Anal Appl 371:764-776, 2010.
  • M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Saddle River, 1976.
  • B. O’Neill, Elementary differential geometry, Academic Press, New York, 1966.
  • 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.
  • G. Canuto, Associated curves and Plücker formulas in Grassmannians , Inventiones Mathematicae , 53 (1) , 77-90, 1979.
  • J.H. Choi, Y.H. Kim, Associated curves of a Frenet curve and their applications. Appl Math Comput, 218: 9116–9124, 2012.
  • 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.
  • 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.
  • E. Özyılmaz, Classical differential geometry of curves according to type-2 Bishop trihedra, Math Comput Appl, 16(4), 858-867, 2011.
There are 11 citations in total.

Details

Primary Language English
Journal Section Issue
Authors

Süha Yılmaz

Publication Date January 8, 2016
Published in Issue Year 2015 Volume: 1 Issue: 1

Cite

APA Yılmaz, S. (2016). CHARACTERIZATIONS OF SOME ASSOCIATED AND SPECIAL CURVES TO TYPE-2 BISHOP FRAME IN E^3. Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi, 1(1), 66-77.