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arXiv · 1401.5847

Cotton tensor and conformal deformations of three-dimensional Ricci flow

Yoshihiro Umehara
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Abstract

We study the deformation of the three-dimensional conformal structures by the Ricci flow. We drive the evolution equation of Cotton-York tensor and the L1-norm of it under the Ricci flow. In particular, we investigate the behavior of the L1-norm of the Cotton-York tensor under the Ricci flow on three-dimensional simply-connected homogeneous manifolds which admit compact quotients. For a non-homogeneous case, we also investigate the behavior of the L1-norm of the Cotton-York tensor for the product metric of the Rosenau solution for the Ricci flow on a two-sphere and the standard metric of a circle.

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Yoshihiro Umehara. 2015-07-17. Cotton tensor and conformal deformations of three-dimensional Ricci flow. https://arxiv.org/abs/1401.5847

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