QR-submanifolds and Riemannian metrics with $G_2$ holonomy

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.

5 pages

References in corpus (2)

• Deformations in G_2 Manifolds
• A CR twistor space of a G2-manifold