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

Kerin, Martin

Abstract

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.

Citation

Kerin, M. (2013). A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces. Annals of Global Analysis and Geometry, 43(1), 63-73. https://doi.org/10.1007/s10455-012-9333-1

• Journal Article Type: Article
• Acceptance Date: May 14, 2012
• Online Publication Date: Jun 6, 2012
• Publication Date: 2013-01
• Deposit Date: Nov 15, 2022
• Publicly Available Date: Nov 15, 2022
• Journal: Annals of Global Analysis and Geometry
• Print ISSN: 0232-704X
• Electronic ISSN: 1572-9060
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 1
• Pages: 63-73
• DOI: https://doi.org/10.1007/s10455-012-9333-1
• Public URL: https://durham-repository.worktribe.com/output/1186099