DOI: 10.36890/iejg.1905970 ISSN: 1307-5624

General Helices in the 3-dimensional Dual Space

Ljiljana Primorac Gajčić
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In this paper, we introduce generalized helices in the three-dimensional dual space $D^3$ as dual curves of a real parameter, whose tangent vector makes a constant inner product with a fixed dual vector. Necessary and sufficient conditions for curve to be a dual generalized helix are expressed in terms of the Frenet invariants of the real part. It is shown that there is a family of generalized helices that share the same axis and have identical real parts, while their dual parts differ.

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