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Year 2013, Volume: 6 Issue: 2, 110 - 117, 30.10.2013

Şeyda Kılıçoğlu , H. Hilmi Hacısalihoğlu

Abstract

References

  • [1] Bishop, L.R., There is more than one way to frame a curve. Amer. Math. Monthly, (1975),Vol- ume 82, Issue 3, 246-251.
  • [2] Bukcu, B. and Karacan M.K., Special Bishop Motion and Bishop Darboux Rotation Axis of space curve. Journal of Dynamical Systems and Geometric Theories. (2008), 6(1), 27-34.
  • [3] Catalan, E., Sur les surfaces réglées dont l’aire est un minimum. J. Math. Pure. Appl. , (1842), 7, 203-211.
  • [4] do Carmo, M. P., Differential Geometry of Curves and Surfaces. Prentice-Hall, ISBN 0-13- 212589-7, 1976.
  • [5] do Carmo, M. P., The Helicoid.” §3.5B in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, (1986), pp. 44-45.
  • [6] Eisenhart, Luther P., A Treatise on the Differential Geometry of Curves and Surfaces. Dover, ISBN 0-486-43820-1, 2004.
  • [7] Graves, L. K., Codimension one isometric immersions between Lorentz spaces. Trans. A.M.S., 252 (1979), 367–392.
  • [8] Hanson, A. J., Hui Ma, Parallel Transport Approach To Curve Framing. Indiana University,Techreports- TR425, January 11(1995).
  • [9] Hanson, A. J., Hui Ma, Quaternion Frame Approach to Streamline Visualization. Ieee Trans- actions On Visualization And Computer Graphics, Vol. I , No. 2, June 1995.
  • [10] Körpınar T. and Ba¸s S., On Characterization Of B-Focal curves In E3. Bol. Soc. Paran. Mat. (2013), 31 (1), 175-178.
  • [11] Shifrin T., Differential Geometry: A First Course in Curves and Surfaces. University of Georgia, Preliminary Version, 2008.
  • [12] Springerlink, Encyclopedia of Mathematics. Springer-Verlag, Berlin Heidelberg New York, 2002.

ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE

Year 2013, Volume: 6 Issue: 2, 110 - 117, 30.10.2013

Şeyda Kılıçoğlu , H. Hilmi Hacısalihoğlu

Abstract


Keywords

Bishop frame Weingarten map fundamental forms

References

  • [1] Bishop, L.R., There is more than one way to frame a curve. Amer. Math. Monthly, (1975),Vol- ume 82, Issue 3, 246-251.
  • [2] Bukcu, B. and Karacan M.K., Special Bishop Motion and Bishop Darboux Rotation Axis of space curve. Journal of Dynamical Systems and Geometric Theories. (2008), 6(1), 27-34.
  • [3] Catalan, E., Sur les surfaces réglées dont l’aire est un minimum. J. Math. Pure. Appl. , (1842), 7, 203-211.
  • [4] do Carmo, M. P., Differential Geometry of Curves and Surfaces. Prentice-Hall, ISBN 0-13- 212589-7, 1976.
  • [5] do Carmo, M. P., The Helicoid.” §3.5B in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, (1986), pp. 44-45.
  • [6] Eisenhart, Luther P., A Treatise on the Differential Geometry of Curves and Surfaces. Dover, ISBN 0-486-43820-1, 2004.
  • [7] Graves, L. K., Codimension one isometric immersions between Lorentz spaces. Trans. A.M.S., 252 (1979), 367–392.
  • [8] Hanson, A. J., Hui Ma, Parallel Transport Approach To Curve Framing. Indiana University,Techreports- TR425, January 11(1995).
  • [9] Hanson, A. J., Hui Ma, Quaternion Frame Approach to Streamline Visualization. Ieee Trans- actions On Visualization And Computer Graphics, Vol. I , No. 2, June 1995.
  • [10] Körpınar T. and Ba¸s S., On Characterization Of B-Focal curves In E3. Bol. Soc. Paran. Mat. (2013), 31 (1), 175-178.
  • [11] Shifrin T., Differential Geometry: A First Course in Curves and Surfaces. University of Georgia, Preliminary Version, 2008.
  • [12] Springerlink, Encyclopedia of Mathematics. Springer-Verlag, Berlin Heidelberg New York, 2002.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Şeyda Kılıçoğlu

H. Hilmi Hacısalihoğlu This is me

Publication Date October 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Kılıçoğlu, Ş., & Hacısalihoğlu, H. H. (2013). ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE. International Electronic Journal of Geometry, 6(2), 110-117.
AMA Kılıçoğlu Ş, Hacısalihoğlu HH. ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE. Int. Electron. J. Geom. October 2013;6(2):110-117.
Chicago Kılıçoğlu, Şeyda, and H. Hilmi Hacısalihoğlu. “ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE”. International Electronic Journal of Geometry 6, no. 2 (October 2013): 110-17.
EndNote Kılıçoğlu Ş, Hacısalihoğlu HH (October 1, 2013) ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE. International Electronic Journal of Geometry 6 2 110–117.
IEEE Ş. Kılıçoğlu and H. H. Hacısalihoğlu, “ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE”, Int. Electron. J. Geom., vol. 6, no. 2, pp. 110–117, 2013.
ISNAD Kılıçoğlu, Şeyda - Hacısalihoğlu, H. Hilmi. “ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE”. International Electronic Journal of Geometry 6/2 (October 2013), 110-117.
JAMA Kılıçoğlu Ş, Hacısalihoğlu HH. ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE. Int. Electron. J. Geom. 2013;6:110–117.
MLA Kılıçoğlu, Şeyda and H. Hilmi Hacısalihoğlu. “ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE”. International Electronic Journal of Geometry, vol. 6, no. 2, 2013, pp. 110-7.
Vancouver Kılıçoğlu Ş, Hacısalihoğlu HH. ON THE RULED SURFACES WHOSE FRAME IS THE BISHOP FRAME IN THE EUCLIDEAN 3-SPACE. Int. Electron. J. Geom. 2013;6(2):110-7.