Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds
Kensuke Onda
TL;DR
This paper explores the Ricci flow on 3D Lie groups and constructs 4D Ricci-flat manifolds with specific symmetry properties, advancing understanding of geometric evolution and special metrics.
Contribution
It introduces new Ricci-flat cohomogeneity one metrics related to 3D Lie groups, linking Ricci flow dynamics with Ricci-flat geometry in four dimensions.
Findings
Construction of Ricci-flat cohomogeneity one metrics
Analysis of Ricci flow on 3D Lie groups
Insights into geometric structures of Ricci-flat manifolds
Abstract
We study relation of the Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. In particular, we construct Ricci-flat cohomogeneity one metrics with respect to 3-dimensional Lie groups.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research