A Family of Steady Ricci Solitons and Ricci-flat Metrics
M. Buzano, A. S. Dancer, M. Gallaugher, M. Wang

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 bundles over quaternionic projective space.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research
