English

The Bryant-Salamon G_2 manifolds and hypersurface geometry

Mathematical Physics 2007-05-23 v2 Differential Geometry math.MP

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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Cite

@article{arxiv.math-ph/0605074,
  title  = {The Bryant-Salamon G_2 manifolds and hypersurface geometry},
  author = {Reiko Miyaoka},
  journal= {arXiv preprint arXiv:math-ph/0605074},
  year   = {2007}
}

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8 pages