Ricci flow on homogeneous spaces with two isotropy summands
Maria Buzano
TL;DR
This paper analyzes the Ricci flow on certain homogeneous spaces with two isotropy summands, providing a complete dynamical description and exploring ancient solutions and Einstein metrics.
Contribution
It offers a comprehensive dynamical systems analysis of Ricci flow on homogeneous spaces with two isotropy summands, including existence results for ancient solutions and Einstein metrics.
Findings
Complete description of Ricci flow behavior on these spaces
Conditions for existence of ancient solutions
Relations between ancient solutions and Einstein metrics
Abstract
We consider the Ricci flow equation for invariant metrics on compact and connected homogeneous spaces whose isotropy representation decomposes into two irreducible inequivalent summands. By studying the corresponding dynamical system, we completely describe the behaviour of the homogeneous Ricci flow on this kind of spaces. Moreover, we investigate the existence of ancient solutions and relate this to the existence and non-existence of invariant Einstein metrics.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research