Co-Axial Metrics on the Sphere and Algebraic Numbers

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2024
• Hauptverfasser: Chen, Zhijie, Lin, Chang-Shou, Yang, Yifan
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2024
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212155
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Co-Axial Metrics on the Sphere and Algebraic Numbers. Zhijie Chen, Chang-Shou Lin and Yifan Yang. SIGMA 20 (2024), 040, 30 pages

In this paper, we consider the following curvature equation Δ + eᵘ = 4π ((₀ − 1)δ₀ + (₁−1)δ₁ + ∑ⁿ⁺ᵐⱼ₌₁(′ⱼ − 1)δₜⱼ)in ℝ², () = −2(1+∞)ln|| + O(1) as || → ∞, where ₀, ₁, ∞, and ′ⱼ are positive non-integers for 1 ≤ j ≤ , while ′ⱼ ∈ ℕ≥₂ are integers for + 1 ≤ j ≤ + . Geometrically, a solution gives r...