A geometric heat flow for vector fields

Details A geometric heat flow for vector fields A geometric heat flow for vector fields

2011-07-13

arxiv.org/abs/1107.2698v2

Mathematics

Differential Geometry

11 pages, comments are welcome

Scientific paper

This is an announcement of our work [5] on introducing and studying 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 of this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds. We will study the similar flow in [6] to find holomorphic vector fields on Kahler manifolds.

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