Abstract

The domain Ω⊂ E5 is considered a set of smooth lines such that through a point X⊂Ω passed one line of a given set. The moving frame is a frame of Frenet for the line ω 1 of the given set. Integral lines of the vector fields are formed in the net Σ5 of Frenet. There exist a point on the tangent of the line ω 1. When the point X is shifted in the domain Ω, the point . describes it’s domain in E 5. The partial mapping is defined as such that . Necessary and sufficient conditions in so that the line γ belong to the three-dimensional distribution is a quasi-double line of the pair is established.

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