Geometric flow of $G_{2}$ -structures on $C(S^3\times S^3)$

preprint2014arXivOpen access

We introduce a first order flow of $G_{2}$ -structures and construct its explicit solution in case of a cone over $S^3\!\times\! S^3$ . Also we prove for this situation that starting from certain initial datum the flow deforms corresponding to $G_2$ -structure metric to a conic metric up to homotheties.

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Geometric flow of $G_{2}$ -structures on $C(S^3\times S^3)$

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Geometric flow of G2G_{2}G2​-structures on C(S3×S3)C(S^3\times S^3)C(S3×S3)

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Geometric flow of $G_{2}$ -structures on $C(S^3\times S^3)$