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2020•Journal of the Indonesian Mathematical SocietyOpen access

Normal Developable Surfaces of A Surface Along A Direction Curve

Rashad Abdel-Baky Abdel-Sattar, Yasi̇n Ünlütürk

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Abstract

We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.

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We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.

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Available abstract

We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.

Key concepts: Developable surface, Mathematics, Surface (topology), Gravitational singularity, Geometry, Ruled surface, Euclidean geometry, Uniqueness

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