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A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces

Kerin, Martin (2013) 'A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces.', Annals of Global Analysis and Geometry, 43 (1). pp. 63-73.


In this note it is shown that every 7-dimensional Eschenburg space can be totally geodesically embedded into infinitely many topologically distinct 13-dimensional Bazaikin spaces. Furthermore, examples are given which show that, under the known construction, it is not always possible to totally geodesically embed a positively curved Eschenburg space into a Bazaikin space with positive curvature.

Item Type:Article
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Publisher statement:This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
Date accepted:14 May 2012
Date deposited:15 November 2022
Date of first online publication:06 June 2012
Date first made open access:15 November 2022

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