| Title:
|
Timelike $B_2$-slant helices in Minkowski space $\operatorname{E}_1^4$ (English) |
| Author:
|
Ali, Ahmad T. |
| Author:
|
López, Rafael |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
39-46 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Minkowski space |
| Keyword:
|
timelike curve |
| Keyword:
|
Frenet equations |
| Keyword:
|
slant helix |
| MSC:
|
53B30 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1240.53115 |
| idMR:
|
MR2644453 |
| . |
| Date available:
|
2010-04-22T10:42:44Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/139994 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
