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2015•Journal of Advanced Mechanical Design Systems and ManufacturingOpen access

Spacelike developable surfaces through a common line of curvature in Minkowski 3-space

Caiyun Li, Chun-Gang Zhu, Ren-Hong Wang

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Abstract

This paper studies the problem to construct a spacelike developable surface possessing a given non-null parametric curve as the line of curvature in Minkowski 3-space. By using Frenet frame to express the surface, we derive the necessary and sufficient conditions when the resulting spacelike developable surface is cylinder, cone or tangent surface. Finally, we give some representative examples.

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This paper studies the problem to construct a spacelike developable surface possessing a given non-null parametric curve as the line of curvature in Minkowski 3-space. By using Frenet frame to express the surface, we derive the necessary and sufficient conditions when the resulting spacelike developable surface is cylinder, cone or tangent surface. Finally, we give some representative examples.

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Available abstract

This paper studies the problem to construct a spacelike developable surface possessing a given non-null parametric curve as the line of curvature in Minkowski 3-space. By using Frenet frame to express the surface, we derive the necessary and sufficient conditions when the resulting spacelike developable surface is cylinder, cone or tangent surface. Finally, we give some representative examples.

Key concepts: Developable surface, Frenet–Serret formulas, Minkowski space, Ruled surface, Curvature, Mathematics, Surface (topology), Tangent

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