Translation surfaces according to Bishop frame in Euclidean 3-space

Gulnur Saffak Atalay, Fatma Guler, Emin Kasap

Abstract


In this paper, by using non-planer space curves the translation surfaces are investigated according to Bishop frames in Euclidean 3-space. We have calculated the first and second fundamental quantities. We give the gaussian and mean curvatures of these surfaces according to the first and second Bishop curvatures in Euclidean 3-space. Also, using the Bishop curvatures of generating curves of translation surface, we give the necessary and sufficient conditions for generating curves to be geodesic and asymptotic curves on the surface.

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How to Cite this Article:

Gulnur Saffak Atalay, Fatma Guler, Emin Kasap, Translation surfaces according to Bishop frame in Euclidean 3-space, Journal of Mathematical and Computational Science, Vol 4, No 1 (2014), 50-57

Copyright © 2014 Gulnur Saffak Atalay, Fatma Guler, Emin Kasap. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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