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On the Motion of the Frenet Vectors and Spacelike Ruled Surfaces in the Minkowski 3-Space

Yusuf Yaylı

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Abstract

In this paper, we obtained the distribution parameter of a spacelike ruled surface generated by a spacelike straight line in Frenet trihedron moving along a spacelike curve. We show that the spacelike ruled surface is developable if and only if the base curve is a helix (inclined curve). Furthermore, some theorems are given for the special cases which the line is being tangent, the principal normal and binormal of the base curve.

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In this paper, we obtained the distribution parameter of a spacelike ruled surface generated by a spacelike straight line in Frenet trihedron moving along a spacelike curve. We show that the spacelike ruled surface is developable if and only if the base curve is a helix (inclined curve). Furthermore, some theorems are given for the special cases which the line is being tangent, the principal normal and binormal of the base curve.

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Available abstract

In this paper, we obtained the distribution parameter of a spacelike ruled surface generated by a spacelike straight line in Frenet trihedron moving along a spacelike curve. We show that the spacelike ruled surface is developable if and only if the base curve is a helix (inclined curve). Furthermore, some theorems are given for the special cases which the line is being tangent, the principal normal and binormal of the base curve.

Key concepts: Frenet–Serret formulas, Tangent, Minkowski space, Ruled surface, Mathematical analysis, Surface (topology), Mathematics, Line (geometry)

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