<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Null cartan curves have been studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curves are not considered. In this paper, we study weak <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> and <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> null cartan curve in Minkowski 3-space 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00039_ieq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>E_1^3</tex-math></alternatives></inline-formula>
. We define helix according to Bishop frame in 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00039_ieq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>E_1^3</tex-math></alternatives></inline-formula>
. Furthermore, the necessary and sufficient conditions for the helices in Minkowski 3-space are obtained.</p></abstract>

Null cartan curves have been studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curves are not considered. In this paper, we study weak AW (k) – type and AW (k) – type null cartan curve in Minkowski 3-space 
E13E_1^3
. We define helix according to Bishop frame in 
E13E_1^3
. Furthermore, the necessary and sufficient conditions for the helices in Minkowski 3-space are obtained.

A study on null cartan curve in Minkowski 3-space

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A study on null cartan curve in Minkowski 3-space"}

Null cartan curves have been studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curves are not considered. In...

A study on null cartan curve in Minkowski 3-space

Published Online: Mar 31, 2020

Page range: 413 - 424

Received: May 02, 2019

Accepted: Aug 30, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00039

Keywords
Null cartan curve, AW(k)-type curve, helix

© 2020 Muhammad Abubakar Isah et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A study on null cartan curve in Minkowski 3-space

Published Online: Mar 31, 2020

Page range: 413 - 424

Received: May 02, 2019

Accepted: Aug 30, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00039

KeywordsNull cartan curve, AW(k)-type curve, helix

© 2020 Muhammad Abubakar Isah et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Null cartan curve, AW(k)-type curve, helix