Cotton flow

Date

2008-8-5

Author

Kişisel, Ali Ulaş Özgür
Sarıoğlu, Bahtiyar Özgür
Tekin, Bayram

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Using the conformally-invariant Cotton tensor, we define a geometric flow, the Cotton flow, which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an entropy functional, and study the flow of nine homogeneous spaces both numerically and analytically. In particular, we show that the arbitrarily deformed homogeneous 3-sphere flows into the round 3-sphere. Two of the nine homogeneous geometries, which are degenerated by the Ricci flow, are left intact by the Cotton flow.

Subject Keywords

Ricci flow, Manifolds, Geometries, Metrics

URI

https://hdl.handle.net/11511/28486

Journal

Classical and Quantum Gravity

DOI

https://doi.org/10.1088/0264-9381/25/16/165019

Collections

Department of Mathematics, Article

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Citation Formats

A. U. Ö. Kişisel, B. Ö. Sarıoğlu, and B. Tekin, “Cotton flow,” Classical and Quantum Gravity, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28486.