A family of 3d steady gradient solitons that are flying wings

Abstract

We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension $n\ge 4$, we find a family of ${\mathbb{Z}}_2\times O(n-1)$-symmetric but non-rotationally symmetric n-dimensional steady gradient solitons with positive curvature operator. We show that these solitons are non-collapsed.

25 pages, a figure added, minor changes

References in corpus (1)

• 3d steady Gradient Ricci Solitons with linear curvature decay

Cited by in corpus (2)

• Ancient Ricci flows with asymptotic solitons
• On a dichotomy of the curvature decay of steady Ricci soliton