Non-K\"ahler Expanding Ricci Solitons II

TL;DR

This paper constructs new examples of complete, non-Kähler expanding Ricci solitons with conical asymptotics on manifolds formed by products of Euclidean space and Einstein spaces, and provides numerical evidence for solitons on certain vector bundles.

Contribution

It introduces novel non-Kähler, non-Einstein expanding Ricci solitons with specific geometric structures and asymptotics, expanding the known landscape of Ricci solitons.

Findings

New non-Kähler, non-Einstein expanding Ricci solitons constructed.

Existence of solitons on manifolds with product structures involving Einstein spaces.

Numerical evidence for solitons on vector bundles over quaternionic projective space.

Abstract

We produce new non-K\"ahler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form $\R^2 \times M_2 \times \cdots \times M_r$, where $r \geq 2$ and $M_i$ are arbitrary closed Einstein spaces with positive scalar curvature. We also find numerical evidence for complete expanding solitons on the vector bundles whose sphere bundles are the twistor or ${\rm Sp}(1)$ bundles over quaternionic projective space.