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

Khazhgali Kozhasov

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

Differential Geometry 2014-07-04 v1

Authors: Khazhgali Kozhasov

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.

Keywords

geometric flow $G_2$-structures cone over $S^3\times S^3$ conic metric homotheties

Cite

@article{arxiv.1407.0963,
  title  = {Geometric flow of $G_{2}$-structures on $C(S^3\times S^3)$},
  author = {Khazhgali Kozhasov},
  journal= {arXiv preprint arXiv:1407.0963},
  year   = {2014}
}

Comments

13 pages, 1 figure

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