Article (Scientific journals)
A geometric heat flow for vector fields
Li, Yi; Liu, KeFeng
2015In Science China Mathematics, 58 (4), p. 673-688
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Keywords :
geometric heat flow; Killing vector fields; Yano’s theorem; Navier-Stokes equations; Kazdan-Warner-Bourguignon-Ezin identity
Abstract :
[en] 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 Kähler manifolds will be studied by Li and Liu
Disciplines :
Mathematics
Author, co-author :
Li, Yi ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit ; Shanghai Jiao Tong University > Mathematics
Liu, KeFeng
External co-authors :
yes
Language :
English
Title :
A geometric heat flow for vector fields
Publication date :
April 2015
Journal title :
Science China Mathematics
ISSN :
1869-1862
Publisher :
Springer
Volume :
58
Issue :
4
Pages :
673-688
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 02 February 2017

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