Tubular surface around a Legendre curve in BCV spaces

Abstract

C. Baikousssis, D.E. Blair[1] made a study of Legendre curves in contact metric manifolds. J. I. Inoguchi, T. Kumamoto, N. Ohsugi, and Y. Suyama[2] studied fundamental properties of Heisenberg 3-spaces. M. Belkhelfa, I.E. Hirica, R. Rosca, L. Verstlraelen[6] obtained a complete characterization of surfaces with paralel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces(BCV). In this study, we define the canal surface around Legendre curve with Frenet frame in BCV spaces. Afterwards we investigate tubular surface around Legendre curve curve with Frenet frame. Finally we give some characterizations about special curves lying on tubular surface around Legendre curve.