Reference : A geometric heat flow for vector fields
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/29568
A geometric heat flow for vector fields
English
Li, Yi mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit > ; Shanghai Jiao Tong University > Mathematics]
Liu, KeFeng []
Apr-2015
Science China Mathematics
Springer
58
4
673-688
Yes (verified by ORBilu)
International
1674-7283
1869-1862
[en] geometric heat flow ; Killing vector fields ; Yano’s theorem ; Navier-Stokes equations ; Kazdan-Warner-Bourguignon-Ezin identity
[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
http://hdl.handle.net/10993/29568

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