2025/05/28 by Nikitenko, E. V., Nikonorov, Yu. G.
#51M16 #51M25 #53A04 #53A05 #57N35 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2505.22374
Let us consider the set Ω(\triangle ABC) of all tetrahedra ABCD with a given non-degenerate base ABC in 𝔼3 and D lying outside the plane ABC. Let us denote by Σ(\triangle ABC) the set \(cos α,cos β,cos γ )∈ ℝ3 | ABCD ∈ Ω(\triangle ABC)\, where α=∠ BDC, β=∠ ADC, and γ=∠ ADB. The paper is devoted to the problem of determining of the closure of Σ(\triangle ABC) in ℝ3 and its boundary.