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Original Articles

On the Bour’s Theorem with Respect to Conformal Map in Minkowski Space

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Pages 149-172 | Received 11 May 2012, Accepted 28 Oct 2012, Published online: 03 Jun 2013

References

  • Bour , E. 1862 . Memoire sur le deformation de surfaces . Journal de I’E cole Polytechnique XXXIX Cahier , : 1 – 148 .
  • Bozkurt , Z. , Gök , İ. , Ekmekci , F. N. and Yaylı , Y. 2012 . A conformal approach to Bour’s theorem . Mathematica Aeterna Int. J. Appl. Math , 8 ( 2 ) : 701 – 713 .
  • Boyadzhiev , K. N. 1999 . Spirals and Conchospirals in the Flight of Insects . College Math. J , 30 ( 1 ) : 23 – 31 .
  • Do Carmo , M.P. and Dajczer , M. 1982 . Helicoidal surfaces with constant mean curvature . Tohoku Math.J , 34 : 425 – 435 .
  • Güler , E. , Yaylı , E. and Hacısalihoğlu , H.H. 2010 . Bour’s theorem on Gauss map in 3-Euclidean space . Hacettepe Math.J , 39 ( 4 ) : 515 – 525 .
  • Güler , E. and Vanlı , T. 2006 . Bour’s theorem in Minkowski 3-space . Kyoto J. Math , 46 ( 1 ) : 47 – 63 .
  • Güler , E. and Vanlı , T. 2008 . On the Mean, Gaussian, the Second Gaussian and the Second mean curvature of the helicoidal surfaces with light-like axis in Minkowski-3 Space . Tsukuba Math. J , 32 ( 1 ) : 49 – 65 .
  • Güler , E. 2007 . Bour’s theorem and light-like profile curve . Yokohama Math. J , 54 ( 1 ) : 55 – 77 .
  • Güler , E. 2008 . Bour’s theorem on timelike helicoidal surfaces with (L,L)-type in Minkowski-3 Space . Beykent University J. Sci. Technol., Turkey , 2 ( 1 ) : 86 – 98 .
  • Hacısalihoğlu , H.H. 2004 . Diferensiyel Geometri , Turkey : Inönü universty Faculty of Science and Arts Press .
  • Ikawa , T. 2001 . Bour’s theorem ın Minkowski Geometry . Tokyo Math.J , 24 ( 2 ) : 377 – 394 .
  • Ikawa , T. 2000 . Bour’s theorem and Gauss map . Yokohama Math. J , 48 ( 2 ) : 173 – 180 .
  • Lopez , R. 2008 . Differential Geometry of Curves and Surfaces in Lorentz Minkowski Space
  • O’neill , Barrett . 1966 . Elementary Differential Geometry , New York : Academic Press .
  • O’neill , Barrett . 1983 . Semi-Riemannian Geometry with Applications to Relativity , Academic Press .
  • Ikawa , T. 1996 . An Introduction To Lorentz Surfaces , Rutgers Uni .
  • Whittemore , J.K. Spiral mimimal surfaces , Trans. Amer. Math. Soc Vol. 19 ,

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