A heat flow for special metrics

Details A heat flow for special metrics A heat flow for special metrics

2009-12-02

arxiv.org/abs/0912.0421v3

Mathematics

Differential Geometry

35 pages, slightly revised

Scientific paper

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently $C^\infty$-close to a critical point.

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