Existence of quasidouble lines of a pair (f15,Δ(135)) in Euclidean space E5

• Published in: Journal of physics. Conference series 2021-07, Vol.1988 (1), p.12082
• Main Authors: Matieva, Gulbadan, Abdullayeva, Cholpon, Artykova, Zhyldyz
• Format: Article
• Language: English
• Subjects: cyclic net of Frenet; Domains; Euclidean geometry; Euclidean space; Fields (mathematics); Frenet frame; partial mapping; pseudo focus; quasi double line
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1988/1/012082

The domain Ω⊂ E 5 is considered a set of smooth lines such that through a point X⊂Ω passed one line of a given set. The moving frame ℜ ( X , e → i ) , ( i , j , k = 1 , 2 , 3 , 4 ) is a frame of Frenet for the line ω 1 of the given set. Integral lines of the vector fields e → i are formed in the net Σ 5 of Frenet. There exist a point F 1 5 ∈ ( X , e → 1 ) on the tangent of the line ω 1 . When the point X is shifted in the domain Ω, the point F 1 5 . describes it’s domain Ω 1 5 in E 5 . The partial mapping is defined as f 1 5 : Ω → Ω 1 5 such that f 1 5 ( X ) = F 1 5 . Necessary and sufficient conditions in so that the line γ belong to the three-dimensional distribution Δ ( 135 ) = ( X , e → 1 , e → 3 , e → 5 ) is a quasi-double line of the pair Δ ( 135 ) = ( F 1 5 , Δ ( 135 ) ) is established.