On steady and expanding Ricci solitons with asymptotic symmetries

We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant’s expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.