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Results on coupled Ricci and harmonic map flows
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Michael Bradford Williams
Published/Copyright:
January 14, 2015
Abstract We explore the harmonic-Ricci flow - that is, Ricci flow coupled with harmonic map flow - both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate that one natural geometric context for the flow is a special case of the locally ℝN-invariant Ricci flow of Lott, and provide examples of gradient solitons for the flow. We prove a version of Hamilton’s compactness theorem for the flow, and then generalize it to the category of étale Riemannian groupoids. Finally, we provide a detailed example of solutions to the flow on the Lie group Nil3.
Received: 2013-1-11
Revised: 2013-5-20
Published Online: 2015-1-14
Published in Print: 2015-1-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
Keywords for this article
Ricci flow;
harmonic map flow;
compactness theorem;
solitons;
Riemannian groupoids
Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
