IJPAM: Volume 15, No. 4 (2004)
FOR CURVES OF THE HEISENBERG GROUP
Department of Mathematics
Faculty of Art and Science
23119 Elazig, TURKEY
Abstract.T. Ikawa obtained in  the following characteristic ordinary differential equation for the circular helix which corresponds to the case that the curvatures and of a time-like curve on the Lorentzian manifold M are constant.
N. Ekmekçi and H. H. Hacisalihoglu generalized in  T. Ikawa's this result, i.e. and are variable, but is constant.
Recently, N. Ekmekçi and K. Ilarslan obtained characterizations of timelike null helices in terms of principalnormal or binormal vector fields .
Furthermore, in  H.Balgetir, M.Bektas and M.Ergüt obtained a geometric characterization of null Frenet curve with constant ratio of curvature and torsion (called null general helix).
In this paper, we obtained characterizations of helices in terms of binormal
vector field for a curve with respect to the Frenet frame of the
three-dimensional Heisenberg group
Received: July 5, 2004
AMS Subject Classification: 53B30
Key Words and Phrases: Heisenberg group, general helix
Source: International Journal of Pure and Applied Mathematics