Title:
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.