O(2)-symmetry of 3D steady gradient Ricci solitons
Abstract: For any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic to a ray we prove that it must be isometric to the Bryant soliton. Otherwise, it is asymptotic to a sector and called a flying wing. We show that all flying wings are O(2)-symmetric. Hence, all 3D steady gradient Ricci solitons are O(2)-symmetric.