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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 6, Pages 1366–1374
DOI: https://doi.org/10.17377/smzh.2015.56.613 (Mi smj2719) 		 
A geometric flow in the space of $G_2$-structures on the cone over $S^3\times S^3$

Kh. Zh. Kozhasovab

a Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
b Sobolev Institute of Mathematics, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/smzh.2015.56.613
Abstract: We consider a flow of $G_2$-structures on a $7$-dimensional manifold admitting a $G_2$-structure. The general solution to this flow is found in the case when the manifold is the cone over $S^3\times S^3$. We prove the convergence of the metric associated with the solution to the conical metric modulo homotheties.
Keywords: $G_2$-structure, $G_2$-manifold flow of $G_2$-structures, cone over $S^3\times S^3$.
Received: 03.07.2014
Revised: 17.08.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 6, Pages 1093–1100
DOI: https://doi.org/10.1134/S0037446615060130
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: Russian
Citation: Kh. Zh. Kozhasov, “A geometric flow in the space of $G_2$-structures on the cone over $S^3\times S^3$”, Sibirsk. Mat. Zh., 56:6 (2015), 1366–1374; Siberian Math. J., 56:6 (2015), 1093–1100
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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