A geometric flow in the space of G 2-structures on the cone over S 3×S 3
- 49 Downloads
We consider a flow of G 2-structures on a 7-dimensional manifold admitting a G 2-structure. The general solution to this flow is found in the case when the manifold is the cone over S 3×S 3. Weprove the convergence of the metric associated with the solution to the conical metric modulo homotheties.
KeywordsG2-structure G2-manifold flow of G2-structures cone over S3×S3
Unable to display preview. Download preview PDF.
- 6.Bryant R. L., “Some remarks on G 2-structures,” Proc. Gokova Geometry–Topology Conf., 2005, pp. 75–109.Google Scholar
- 8.Bryant R. L. and Xu Feng, “Laplacian flow for closed G 2-structures: Short Time Behavior,” arXiv article, 11 Jan 2011, arXiv:math.DG/1101.2004v1.Google Scholar
- 10.Joyce D. D., Compact Manifolds with Special Holonomy, Oxford Univ. Press, Oxford (2000) (Oxford Math. Monographs).Google Scholar