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arXiv:1104.4895 [math.DG]AbstractReferencesReviewsResources

QR-submanifolds and Riemannian metrics with $G_2$ holonomy

Dmitry Egorov

Published 2011-04-26, updated 2011-07-05Version 2

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.

Comments: 5 pages
Journal: Mathematical Notes, 2011, 90:5, 763-766
Categories: math.DG
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