Timelike B 2 -slant helices in Minkowski space E 1 4

Ahmad T. Ali; Rafael López

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 1, page 39-46
  • ISSN: 0044-8753

Abstract

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We consider a unit speed timelike curve α in Minkowski 4-space 𝐄 1 4 and denote the Frenet frame of α by { 𝐓 , 𝐍 , 𝐁 1 , 𝐁 2 } . We say that α 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 𝐄 1 4 . In this work we study those helices where the function 〈 𝐁 2 , U 〉 is constant and we give different characterizations of such curves.

How to cite

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Ali, Ahmad T., and López, Rafael. "Timelike $B_2$-slant helices in Minkowski space $\operatorname{E}_1^4$." Archivum Mathematicum 046.1 (2010): 39-46. <http://eudml.org/doc/37652>.

@article{Ali2010,
abstract = {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.},
author = {Ali, Ahmad T., López, Rafael},
journal = {Archivum Mathematicum},
keywords = {Minkowski space; timelike curve; Frenet equations; slant helix; Minkowski space; timelike curve; Frenet equations; slant helix},
language = {eng},
number = {1},
pages = {39-46},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Timelike $B_2$-slant helices in Minkowski space $\operatorname\{E\}_1^4$},
url = {http://eudml.org/doc/37652},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Ali, Ahmad T.
AU - López, Rafael
TI - Timelike $B_2$-slant helices in Minkowski space $\operatorname{E}_1^4$
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 1
SP - 39
EP - 46
AB - 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.
LA - eng
KW - Minkowski space; timelike curve; Frenet equations; slant helix; Minkowski space; timelike curve; Frenet equations; slant helix
UR - http://eudml.org/doc/37652
ER -

References

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  9. Önder, M., Kazaz, M., Kocayiǧit, H., Kilic, O., B 2 -slant helix in Euclidean 4-space E 4 , Int. J. Contemp. Math. Sci. 3 (29) (2008), 1433–1440. (2008) Zbl1175.14019MR2514022
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