New expanding Ricci solitons starting in dimension four

TL;DR

This paper constructs new examples of gradient expanding Ricci solitons that are asymptotic to cones over certain manifolds, including positive scalar curvature solutions on   S^1, expanding the known landscape of Ricci solitons.

Contribution

It introduces a method to produce gradient expanding Ricci solitons asymptotic to cones over products of Einstein manifolds, including explicit examples with positive scalar curvature.

Findings

Existence of asymptotically conical expanding Ricci solitons over specified cones.

Construction of continuous families of such solitons on trivial vector bundles.

Explicit examples on   S^1 with positive scalar curvature.

Abstract

We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive scalar curvature on $\mathbb{R}^3 \times S^1.$ More generally we construct continuous families of gradient expanding Ricci solitons on trivial vector bundles over products of Einstein manifolds with arbitrary Einstein constants.