Geodesic
O(2)-symmetry of 3D steady gradient Ricci solitons
Lai, Yi1
1Department of Mathematics, Stanford University, Stanford, CA, United States
Geometry & topology, Tome 29 (2025) no. 2, pp. 687-789
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We prove that all 3D steady gradient Ricci solitons are O(2)-symmetric. The O(2)-symmetry is the most universal symmetry in Ricci flows with any type of symmetries. Our theorem is also the first instance of symmetry theorem for Ricci flows that are not rotationally symmetric. We also show that the Bryant soliton is the unique 3D steady gradient Ricci soliton with positive curvature that is asymptotic to a ray.

DOI : 10.2140/gt.2025.29.687
Keywords: Ricci flow, Ricci soliton, 3D steady soliton, flying wing, $O(2)$-symmetric, symmetry improvement, Killing field, Ricci De Turck flow, asymptotic cone, dimension reduction, uniqueness of Bryant soliton, cigar soliton, collapsed soliton

Lai, Yi  1

1 Department of Mathematics, Stanford University, Stanford, CA, United States 
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Lai, Yi. O(2)-symmetry of 3D steady gradient Ricci solitons. Geometry & topology, Tome 29 (2025) no. 2, pp. 687-789. doi: 10.2140/gt.2025.29.687

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