Abstract
AbstractWe give a shorter proof of the well-posedness of the Laplacian flow in $${\rm G}_2$$
G
2
-geometry. This is based on the observation that the DeTurck–Laplacian flow of $${\mathrm{G}}_2$$
G
2
-structures introduced by Bryant and Xu as a gauge fixing of the Laplacian flow can be regarded as a flow of (not necessarily closed) $${\mathrm{G}}_2$$
G
2
-structures, which fits in the general framework introduced by Hamilton in J Differ Geom 17(2):255–306, 1982. A similar application is given for the modified Laplacian co-flow.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Reference5 articles.
1. Bryant, R.: Some remarks on $$\text{G}_2$$-structures. In: Proceedings of Gokova Geometry/Topology Conference, Gokova, pp. 75–109 (2006)
2. Bryant, R., Xu, F.: Laplacian Flow for Closed $${\rm G}_2$$-Structures: Short Time Behavior. arXiv:1101.2004
3. Grigorian, S.: Short-time behaviour of a modified Laplacian coflow of $${\rm G}_2$$-structures. Adv. Math. 248, 378–415 (2013)
4. Hamilton, R.S.: Three-manifolds with positive Ricci curvature. J. Differential Geom. 17(2), 255–306 (1982)
5. Karigiannis, S., McKay, B., Tsui, M.-P.: Soliton solutions for the Laplacian coflow of some $${\rm G}_2$$ structures with symmetry. Differential Geom. Appl. 30, 318–333 (2012)
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