Involute Curve of the Biharmonic Curve in the （渐开线曲线的双调和的曲线）.pdfVIP

Gen. Math. Notes, Vol. 2, No. 1, January 2011, pp. 175-185 ISSN 2219-7184; Copyright © ICSRS Publication, 2011 Available free online at http://www.geman.in Involute Curve of the Biharmonic Curve in the Special Three-Dimensional Kenmotsu Manifold K with η -Parallel Ricci Tensor 1 2 3 Talat Körpınar , Essin Turhan and Iqbal H. Jebril 1,2 Fırat University, Department of Mathematics, 23119, Elazığ, Turkey E-mail 1 : talatkorpinar@ E-mail 2 : essin.turhan@ 3 Department of Mathematics, King Faisal University, Saudi Arabia e-mail 3 : iqbal501@ (Received 07.12.2010, Accepted 25.01.2011) Abstract In this paper, we study involute curve of the biharmonic curve in the special three-dimensional Kenmotsu manifold K with η -parallel ricci tensor. We characterize involute curve by means of biharmonic curves in the special three- dimensional Kenmotsu manifold K with η -parallel ricci tensor. Keywords: biharmonic curve, involute curve, Kenmotsu manifold. 2000 MSC No: 53C41, 53A10. Talat Körpınar et al. 176 1 Introduction The idea of a string involute is due to C. Huygens (1658), who is also known for his work in optics. He discovered involutes while trying to build a more accurate clock (see [2]). The involute of a given curve is a well-known 3 concept in Euclidean-3 space E . An evolute and its involute, are defined in mutual pairs. The evolute of any curve is defined as the lo