A heat flow for special metrics
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2009
- DOI:
- 10.48550/arXiv.0912.0421
- arXiv:
- arXiv:0912.0421
- Bibcode:
- 2009arXiv0912.0421W
- Keywords:
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- Mathematics - Differential Geometry;
- 53C44;
- 53C25
- E-Print:
- 35 pages, slightly revised