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Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces

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Abstract

In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike ruled surface. By the aid of the E. Study Mapping, we consider timelike ruled surfaces as dual hyperbolic spherical curves and define the Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We obtain the relationships between invariants of Mannheim timelike surface offsets. Furthermore, we give the conditions for these surface offsets to be developable.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Celal Bayar University, Muradiye Campus, Muradiye, Manisa, Turkey

    Mehmet Önder

  2. Department of Secondary Education Science and Mathematics Teaching, Mathematics Teaching Program, Faculty of Education, Gazi University, Ankara, Turkey

    H. Hüseyin Uğurlu

Authors
  1. Mehmet Önder
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  2. H. Hüseyin Uğurlu
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Correspondence to Mehmet Önder.

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Önder, M., Uğurlu, H.H. Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 83, 163–169 (2013). https://doi.org/10.1007/s40010-013-0067-7

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  • DOI: https://doi.org/10.1007/s40010-013-0067-7

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