Rotational symmetry of non negatively curved expanding gradient Ricci solitons

2013/03/14 by Deruelle, Alix
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.3446

Abstract

Let (Mⁿ,g,∇ f), n≥ 3, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to C(\mathbbS^n-1(c)) where \mathbbS^n-1(c) is the standard (n-1)-sphere of curvature 1/c², with c∈(0,1). We prove that if the convergence to the asymptotic cone is smooth, (Mⁿ,g,∇ f) is rotationally symmetric. This is the expanding analogue of the Perelman conjecture on the Bryant soliton and this work is based on the proof by Brendle \citeBre-Rot-3d. This has also been proved recently by Chodosh \citeCho-EGS.

Related

• Rotational symmetry of Ricci solitons in higher dimensions
• 3d steady Gradient Ricci Solitons with linear curvature decay
• Steady Ricci solitons with horizontally ε-pinched Ricci curvature
• Higher dimensional steady Ricci solitons with linear curvature decay
• On rotationally invariant shrinking gradient Ricci solitons