<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In Lorentz-Minkowski 3-space, null scrolls are ruled surfaces with a null base curve and null rulings. Their mean, as well as their Gaussian curvature, depends only on a parameter of a base curve. In the present paper, we obtain the first-order nonlinear differential equation (Riccati equation) which relates curvatures of a base curve to curvatures of a null scroll. Conditioned by this equation, we can determine a family of null scrolls with a given null base curve and prescribed curvatures, in particular, a family of minimal and constant mean curvature null scrolls.</p></abstract>

In Lorentz-Minkowski 3-space, null scrolls are ruled surfaces with a null base curve and null rulings. Their mean, as well as their Gaussian curvature, depends only on a parameter of a base curve. In the present paper, we obtain the first-order nonlinear differential equation (Riccati equation) which relates curvatures of a base curve to curvatures of a null scroll. Conditioned by this equation, we can determine a family of null scrolls with a given null base curve and prescribed curvatures, in particular, a family of minimal and constant mean curvature null scrolls.

Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space

Department of Mathematics, Faculty of Science

Faculty of Mining, Geology and Petroleum Engineering

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space"}

In Lorentz-Minkowski 3-space, null scrolls are ruled surfaces with a null base curve and null rulings. Their mean, as well as their Gaussian curvature, depends...

Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space

Published Online: Dec 28, 2020

Page range: 229 - 240

Received: Jan 22, 2020

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/auom-2020-0043

Keywords
Null scroll, prescribed curvature, Lorentz-Minkowski space

© 2020 Željka Milin Šipuš et al., published by Sciendo

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

Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space

Published Online: Dec 28, 2020

Page range: 229 - 240

Received: Jan 22, 2020

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/auom-2020-0043

KeywordsNull scroll, prescribed curvature, Lorentz-Minkowski space

© 2020 Željka Milin Šipuš et al., published by Sciendo

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

Keywords
Null scroll, prescribed curvature, Lorentz-Minkowski space