A Family of Steady Ricci Solitons and Ricci-flat Metrics

TL;DR

This paper introduces new complete steady Ricci solitons and Ricci-flat metrics with unique asymptotic behaviors, providing both explicit examples and numerical evidence for certain geometric structures.

Contribution

It constructs novel non-Kähler steady Ricci solitons with combined asymptotics and a family of Ricci-flat metrics with asymptotically locally conical geometry, plus numerical insights into specific vector bundle structures.

Findings

New non-Kähler steady Ricci solitons with combined asymptotics

A family of Ricci-flat metrics with asymptotically locally conical geometry

Numerical evidence for steady solitons on specific vector bundles

Abstract

We produce new non-K\"ahler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. We also obtain a family of complete Ricci-flat metrics with asymptotically locally conical asymptotics. Finally, we obtain numerical evidence for complete steady soliton structures on the vector bundles whose distance sphere bundles are respectively the twistor and ${\rm Sp}(1)$ bundles over quaternionic projective space.