Geometric flow of $G_2$-structures on $C(S^3\times S^3)$

Abstract

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.

arXiv comment13 pages, 1 figure