Tubular surface around a Legendre curve in BCV spaces

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.

Keywords:

Canal surfaces, tubular surfaces, connections, geodesics Sasaki spaces,

PDF

___

Baikousssis, C., Blair, D.E. On Legendre Curves in Contact 3-manifolds. Geometriae Dedicata 49; 135-142, (1994).
Belkhelfa, M., Hırıca, E., Rosca, R. and Verstraelen, L., On Legendre Curves In Rıemannıan And Lorentzıan Sasakı Spaces, Soochow Journal Of Mathematıcs, Volume 28, No. 1, pp. 81-91, January (2002).
Bianchi, L. , Lezioni Di Geometrie Differenziale, E. Spoerri Librario-Editore. (1894). Bianchi, L. , Lezioni Sulla Teoria Dei Gruppi Continui E Finiti Di Transformazioni, Ed. Zanichelli, (1928).
Bishop, R. L., There is more than one way to frame a curve, Amer. Math. Monthly, Volume 82, Issue 3 (1975), 246-251.
Blair, D.E., Riemannian Geometry of Contact and Symplectic Manifolds. Boston (2001).
Cartan, E. Lecons Sur La Geometria Des Espace De Riemann. Gauthier Villars, Paris, (1894).
Doğan, F. and Yaylı, Y., On the curvatures of tubular surface with Bishop frame, Commun. Fac. Sci. Univ. Ank. Series A1 Volume 60, 1 (2011), 59-69.
Gross, A., Analyzing generalized tubes, Siam Rev. 30, 1-68, (1988).
Hacısaliho˘glu, H. H., Differensiyel Geometri II, Hacısaliho˘glu Yayınları(2000).
Inoguchi, J.I., Kumamoto, T., Ohsugi, N., Suyama, Y. Differential Geometry of Curves and Surfaces in 3-dimensional Homogeneous Spaces 1. Fukuoka University Science, Reports, 29(2); 155-182, (1999) 
Maekawa, T., Patrikalakis, M. N., Sakkalis, T. and Yu, G., Yu, Analysis and applications of pipe surfaces, Computer Aided Geometric Design 15 (1998), 437-458.
Oprea, J., Differential Geometry and Its Applications, Prentice-Hall Inc., (1997).
Vranceanu, G., Lec¸ons De Geometrie Differentielle I.Ed.Acad.Rep.Pop. Roum, Bucarest, (1947).
Xu, Z., Feng, R. and Sun, G.J., Analytic and algebraic properties of canal surfaces, Journal of Computational and Applied Mathematics, 195 (2006), 220-228.
Yıldırım, A., Differential Geometry of Curves on Homogeneous Spaces, Phd Thesis, University of Ankara, (2005).