Timelike Tangent Developable Surfaces and Bonnet Surfaces

• Published in: Abstract and Applied Analysis Vol. 2016; no. 2016; pp. 453 - 459
• Main Authors: Ersoy, S., Eren, Kemal
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 2016; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Constants; Criteria; Curvature; Flats; Lithium; Mathematical analysis; Tangents; Torsion; United States
• ISSN: 1085-3375; 1687-0409
• DOI: 10.1155/2016/6837543

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.