Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space-Reference-Cited by-同舟云学术

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

Published:2020-12-01 Issue:3 Volume:28 Page:229-240
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Šipuš Željka Milin¹,Gajčić Ljiljana Primorac²,Protrka Ivana³

Affiliation:

1. Department of Mathematics, Faculty of Science , University of Zagreb , Bijenička cesta 30, 10000 Zagreb , Croatia .

2. Department of Mathematics , University of Osijek , Trg Ljudevita Gaja 6 , Croatia .

3. Faculty of Mining, Geology and Petroleum Engineering , University of Zagreb , Pierottijeva ul. 6, 10000 Zagreb , Croatia .

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2020-0043

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