We give a shorter proof of the well-posedness of the Laplacian flow in $${\rm G}_2$$ -geometry. This is based on the observation that the DeTurck–Laplacian flow of $${\mathrm{G}}_2$$ -structures introduced by Bryant and Xu as a gauge fixing of the Laplacian flow can be regarded as a flow of (not necessarily closed) $${\mathrm{G}}_2$$ -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.

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关于 $${\mathrm{G}}_2$$-geometry 中拉普拉斯流和修正拉普拉斯协流的评论

我们给出了 $${\rm G}_2$$ -geometry 中拉普拉斯流的适定性的简短证明。这是基于观察到 $${\mathrm{G}}_2$$ - 结构的 DeTurck-Laplacian 流由 Bryant 和 Xu 引入作为拉普拉斯流的规范固定可以被视为（不一定关闭）$${\mathrm{G}}_2$$ -structures，它符合 Hamilton 在 J Differ Geom 17(2):255–306, 1982 中引入的一般框架。对于改进的 Laplacian 给出了类似的应用同流。