Constant pseudo-angle lightlike surfaces

Abstract

The oriented angles between lightlike vectors cannot be defined properly compared to the timelike vectors in the Minkowski spacetime. Therefore, we use the pseudo-angles between any non-lightlike or lightlike vectors to develop the theory of lightlike surfaces having constant angle with a fixed nonlightlike direction. We investigate some geometric properties on these surfaces such as being a tangent developable. Besides, we construct the constant angle lightlike ruled surfaces by means of the null helices. We give several examples to illustrate the obtained surfaces.

Keywords

• Lightlike surface
• pseudo-angle
• transversal vector field
• ruled surface
• Cartan slant helix
• null helix
• pseudo-null curve.

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