Existence of quasidouble lines of a pair (f15,Δ(135)) in Euclidean space E5
Gulbadan Matieva, Cholpon Abdullayeva, Жылдыз Артыкова · Journal of Physics Conference Series · 2021
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 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 Σ5 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 ,