On $G_2$-structures, special metrics and related flows

Abstract

We review results about $G_2$-structures in relation to the existence of special metrics, such as Einstein metrics and Ricci solitons, and the evolution under the Laplacian flow on non-compact homogeneous spaces. We also discuss some examples in detail.

arXiv commentTo appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"

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