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

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

2012-03-09

arxiv.org/abs/1203.2124v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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