A note on Lamarle formula in Minkowski $3$-space

The Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field in Minkowski...

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Bibliographic Details
Published inTamkang journal of mathematics Vol. 49; no. 4; pp. 291 - 300
Main Authors Öztürk, Ufuk, İlarslan, Kazım, Koç Öztürk, Esra Betül, Nesovic, Emilija
Format Journal Article
LanguageEnglish
Published 01.12.2018
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Summary:The Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field in Minkowski $3$-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples.
ISSN:0049-2930
2073-9826
DOI:10.5556/j.tkjm.49.2018.2653