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SLANT HELICES IN MINKOWSKI SPACE E13

  • Ali, Ahmad T. (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE KING ABDUL AZIZ UNIVERSITY, MATHEMATICS DEPARTMENT FACULTY OF SCIENCE) ;
  • Lopez, Rafael (DEPARTAMENTO DE GEOMETRIA Y TOPOLOGIA UNIVERSIDAD DE GRANADA)
  • Received : 2009.05.22
  • Published : 2011.01.01

Abstract

We consider a curve $\alpha$= $\alpha$(s) in Minkowski 3-space $E_1^3$ and denote by {T, N, B} the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction U of $E_1^3$ such that the function is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $E_1^3$.

Keywords

Minkowski 3-space;Frenet equations;slant helix

References

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