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A Conformal Approach to Bour's Theorem

Journal Name:

  • Mathematica Æterna

Publication Year:

  • 2012

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, we give relation between Bour's theorem and confor- mal map in Euclidean 3space. We prove that a spiral surface and a helicoidal surface have a conformal relation. So, a helix on the helicoid correspond to a spiral on the spiral surface. Moreover we obtain that a spiral surface and a rotation surface have a conformal relation. So, spirals on the spiral surface correspond to parallel circles on the rotation surface. When the conformal map is an isometry we obtain the Bour's theorem ,i.e, we obtain an isometric relation between the helisoidal sur- face and the rotation surface, which was given by Bour in [1]. Thus this paper is a generalization of Bour's theorem.
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  • 8
701-713
  • English

REFERENCES

References: 

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712 Z.BOZKURT, I˙ GO¨K, F. N. EKMEKCI˙ and Y. YAYLI
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College Math. J., 30 (1999) 1, 23{31.
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[8] E. Guler, Bour's theorem on timelike helicoidal surfaces with (L; L)-type
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[9] H. H. Hacsalihoglu, Dierential Geometry, (Inonu universty Faculty of
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[10] T. Ikawa, Bour's theorem n Minkowski Geometry, Tokyo Math.J. 24(2),
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[12] B. O'Neil, Elementary Dierential Geometry (Academic Press, New York,
1966).

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