Position vectors of a spacelike general helices in Minkowski Space $\e_1^3$

Details Position vectors of a spacelike general helices in Minkowski Space $\e_1^3$ Position vectors of a spacelike general helices in Minkowski Space $\e_1^3$

2009-08-03

arxiv.org/abs/0908.0041v1

Mathematics

Differential Geometry

15 pages, 3 figures

Scientific paper

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrinsic equations. Moreover, we give some examples to illustrate how to find the position vectors of a spacelike general helices with a spacelike and timelike principal normal vector from the intrinsic equations.

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