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A geometric heat flow for vector fields

Yi Li Kefeng Liu

Differential Geometry mathscidoc:1912.43104

Science China Mathematics, 58, (4), 673-688, 2015.4
We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on Khler manifolds will be studied by Li and Liu (2014).
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@inproceedings{yi2015a,
  title={A geometric heat flow for vector fields},
  author={Yi Li, and Kefeng Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111553839084664},
  booktitle={Science China Mathematics},
  volume={58},
  number={4},
  pages={673-688},
  year={2015},
}
Yi Li, and Kefeng Liu. A geometric heat flow for vector fields. 2015. Vol. 58. In Science China Mathematics. pp.673-688. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111553839084664.
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