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 $n \geq 4$, 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.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar