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arXiv · 1104.4895

QR-submanifolds and Riemannian metrics with $G_2$ holonomy

Dmitry Egorov
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Abstract

In this note we prove that QR-submanifolds of the hyper-Kahler manifolds under some conditions admit the $G_2$ holonomy. We give simplest examples of such QR-submanifolds namely tori. We conjecture that all $G_2$ holonomy manifolds arise in this way.

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Dmitry Egorov. 2011-04-26. QR-submanifolds and Riemannian metrics with $G_2$ holonomy. https://arxiv.org/abs/1104.4895

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