2012
DOI: 10.1007/s10455-012-9333-1
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A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces

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.

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Cited by 2 publications
(2 citation statements)
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“…• there exists an S-fibration with the same data M, Σ, F, G, p, q, r as of the fibration W 7 2 → CP 2 such that it is obtained from a fiber-wise action of U (1) on the trivial bundle S 5 × S 3 → S 5 such that it has the same value of the characteristic class κ as the S-fibration W 7 2 → CP 2 .…”
Section: Theorem 1 the Projectionmentioning
confidence: 99%
See 1 more Smart Citation
“…• there exists an S-fibration with the same data M, Σ, F, G, p, q, r as of the fibration W 7 2 → CP 2 such that it is obtained from a fiber-wise action of U (1) on the trivial bundle S 5 × S 3 → S 5 such that it has the same value of the characteristic class κ as the S-fibration W 7 2 → CP 2 .…”
Section: Theorem 1 the Projectionmentioning
confidence: 99%
“…This work was devoted to totally geodesic embeddings of positively curved 7-spaces into 13-dimensional spaces of positive curvature (the choice of dimensions is due to known examples) and their relation to the pinching constants of metrics. In the article we obtained the very first results on this problem which later was studied in[5,6,7].…”
mentioning
confidence: 99%