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Totally geodesic embeddings of 7-manifolds in positively curved 13-manifolds

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Abstract.

We demonstrate a correspondence between the set of Bazaikin spaces with a subset of Aloff-Wallach and Eschenburg spaces. We show that each Bazaikin space contains at least one and generically 10 totally geodesically embedded Aloff-Wallach or Eschenburg spaces. We use these embeddings to get a sharp upper bound for the pinching of the standard biquotient metrics over the whole family of Bazaikin spaces, and to characterise the curvature properties and regularity of the Bazaikin space in terms of the curvature and regularity of the embedded spaces.

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Authors and Affiliations

  1. Westfälisches Wilhelms-Universität, Mathematisches Institut, Einsteinstrasse 62, 48149, Münster, Germany

    Owen Dearricott

  2. Institut für Mathematik, Universität, Augsburg, 86135, Augsburg, Germany

    Jost-Hinrich Eschenburg

Authors
  1. Owen Dearricott
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  2. Jost-Hinrich Eschenburg
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Correspondence to Owen Dearricott.

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Mathematics Subject Classification (2000): 53C20, 53C30, 53C40

Acknowledgements. It is a pleasure for us to thank I. Taimanov and W. Ziller for valuable hints and discussion.

Dedicated to Ernst Heintze on occasion of his 60th birthday

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Dearricott, O., Eschenburg, JH. Totally geodesic embeddings of 7-manifolds in positively curved 13-manifolds. manuscripta math. 114, 447–456 (2004). https://doi.org/10.1007/s00229-004-0470-0

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  • DOI: https://doi.org/10.1007/s00229-004-0470-0

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