QR-submanifolds and Riemannian metrics with $G_2$ holonomy

Details QR-submanifolds and Riemannian metrics with $G_2$ holonomy QR-submanifolds and Riemannian metrics with $G_2$ holonomy

2011-04-26

arxiv.org/abs/1104.4895v2

Mathematical Notes, 2011, 90:5, 763-766

Mathematics

Differential Geometry

5 pages

Scientific paper

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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