Original scientific paper

Lamarle formula in 3-dimensional Lorentz space

Soley Ersoy orcid.org/0000-0002-7183-7081 ; Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, Turkey
Murat Tosun ; Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, Turkey

Abstract

The Lamarle Formula is known as a
relationship between the Gaussian curvature and the distribution parameter (Drall)
of a ruled surface in the surface theory, \cite{Kr}. In $\mathbb{R}_{1}^{3}$, the
non-null ruled surfaces were investigated
in five different classes with respect to the character of base
curves and rulings, [8]-[10]. In this paper, by
excluding the null tangent of ruling, three different kinds of
non-null ruled are taken into consideration and the relationships
between the Gaussian curvatures and distribution parameters of
spacelike ruled surface, timelike ruled surface with spacelike
ruling and timelike ruled surface with timelike ruling are
obtained, respectively. These relationships are called as
Lorentzian Lamarle formulae. Finally, some examples concerning
these relations are given.

Keywords

Ruled surface; distribution parameter (Drall); Gaussian curvature; Lamarle formula

Hrčak ID:

74903

URI

https://hrcak.srce.hr/74903

Publication date:

21.12.2011.

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