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Abstract and Applied Analysis
Volume 2016, Article ID 6837543, 7 pages
http://dx.doi.org/10.1155/2016/6837543
Research Article

Timelike Tangent Developable Surfaces and Bonnet Surfaces

Department of Mathematics, Faculty of Arts and Science, Sakarya University, 54187 Sakarya, Turkey

Received 20 November 2015; Accepted 3 January 2016

Academic Editor: Chun-Gang Zhu

Copyright © 2016 Soley Ersoy and Kemal Eren. 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.

Abstract

A criterion was given for a timelike surface to be a Bonnet surface in 3-dimensional Minkowski space by Chen and Li, 1999. In this study, we obtain a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface by the aid of this criterion. This is examined under the condition of the curvature and torsion of the base curve of the timelike developable surface being nonconstant. Moreover, we investigate the nontrivial isometry preserving the mean curvature for a timelike flat helicoidal surface by considering the curvature and torsion of the base curve of the timelike developable surface as being constant.