Ruled invariants and associated ruled surfaces of a space curve

Huili Liu, Yixuan Liu and Seoung Dal Jung

Applied Mathematics and Computation, 2019, vol. 348, issue C, 479-486

Abstract: As we know, a ruled surface is the tangent ruled surface of a space curve if and only if its ruled distance density function vanishes identically; a ruled surface is the binormal ruled surface of a space curve if and only if its ruled translation density function vanishes identically. The ruled distance density function and translation density function are differential invariants of ruled surfaces in three dimensional Euclidean space. In this paper we give the necessary and sufficient condition of which a ruled surface is the principal normal ruled surface of a space curve using the theories of ruled invariants of ruled surface in three dimensional Euclidean space.

Keywords: Ruled invariant; Differential invariant; Structure functions of ruled surface; Frenet ruled surfaces of curve; Principal normal ruled surface of curve (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:479-486

DOI: 10.1016/j.amc.2018.12.011

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