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The Bryant-Salamon G_2 manifolds and hypersurface geometry

Reiko Miyaoka
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Abstract

We show that two of the Bryant-Salamon G_2-manifolds have a simple topology ; homeomorphic to the complement of some submanifolds of the 7-dimensional sphere. In this connection, we show there exists a complete Ricci-flat (non-flat) metric on the complement of an m-dimensional sphere in an n-dimensional sphere for some n-1>m. We also give many examples of special Lagrangian submanifolds of the cotangent bundle of the sphere with the Stenzel metric. Hypersurface geometry is essential in the argument.

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Reiko Miyaoka. 2006-06-02. The Bryant-Salamon G_2 manifolds and hypersurface geometry. https://arxiv.org/abs/math-ph/0605074

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