Geodesic
Timelike $B_2$-slant helices in Minkowski space $\operatorname{E}_1^4$
Archivum mathematicum, Tome 46 (2010) no. 1, pp. 39-46

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We consider a unit speed timelike curve $\alpha $ in Minkowski 4-space ${\mathbf{E}}_1^4$ and denote the Frenet frame of $\alpha $ by $\lbrace {\mathbf{T}}, {\mathbf{N}}, {\mathbf{B}}_1, {\mathbf{B}}_2\rbrace $. We say that $\alpha $ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of ${\mathbf{E}}_1^4$. In this work we study those helices where the function $\langle {\mathbf{B}}_2,U\rangle $ is constant and we give different characterizations of such curves.
Classification : 53B30, 53C50
Keywords: Minkowski space; timelike curve; Frenet equations; slant helix 
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     author = {Ali, Ahmad T. and L\'opez, Rafael},
     title = {Timelike $B_2$-slant helices in {Minkowski} space $\operatorname{E}_1^4$},
     journal = {Archivum mathematicum},
     pages = {39--46},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2010},
     mrnumber = {2644453},
     zbl = {1240.53115},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_1_a3/}
}
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Ali, Ahmad T.; López, Rafael. Timelike $B_2$-slant helices in Minkowski space $\operatorname{E}_1^4$. Archivum mathematicum, Tome 46 (2010) no. 1, pp. 39-46. http://geodesic.mathdoc.fr/item/ARM_2010__46_1_a3/