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Examples for cross curvature flow on 3-manifolds

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Abstract

Recently, B. Chow and R.S. Hamilton [3] introduced the cross curvature flow on 3-manifolds. In this paper, we analyze two interesting examples for this new flow. One is on a square torus bundle over a circle, and the other is on a S 2 bundle over a circle. We show that the global flow exists in both cases. However, on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua university, Beijing, 100084, China

    Li Ma & Dezhong Chen

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  1. Li Ma
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  2. Dezhong Chen
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Correspondence to Li Ma.

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Mathematics Subject Classification (1991) 53C44

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Ma, L., Chen, D. Examples for cross curvature flow on 3-manifolds. Calc. Var. 26, 227–243 (2006). https://doi.org/10.1007/s00526-005-0366-1

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  • DOI: https://doi.org/10.1007/s00526-005-0366-1

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