Ricci flow on three-dimensional manifolds with symmetry
John Lott, Natasa Sesum
TL;DR
This paper studies the behavior of Ricci flow on specific classes of three-dimensional manifolds with symmetry, focusing on warped products and manifolds with U(1) x U(1) actions, to understand their geometric evolution.
Contribution
It provides a detailed analysis of Ricci flow on two classes of symmetric 3D manifolds, extending understanding of geometric evolution in symmetric settings.
Findings
Describes Ricci flow behavior on warped product manifolds.
Analyzes Ricci flow on manifolds with U(1) x U(1) symmetry.
Provides insights into geometric evolution of symmetric 3D manifolds.
Abstract
We describe the Ricci flow on two classes of compact three-dimensional manifolds: 1. Warped products with a circle fiber over a two-dimensional base. 2. Manifolds with a free local isometric U(1) x U(1) action.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Neuroimaging Techniques and Applications