Trinca, Federico;
(2023)
Cayley fibrations in the Bryant–Salamon Spin(7) manifold.
Annali di Matematica Pura ed Applicata (1923 -)
, 202
(3)
pp. 1131-1171.
10.1007/s10231-022-01273-z.
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Abstract
On each complete asymptotically conical Spin (7) manifold constructed by Bryant and Salamon, including the asymptotic cone, we consider a natural family of SU (2) actions preserving the Cayley form. For each element of this family, we study the (possibly singular) invariant Cayley fbration, which we describe explicitly, if possible. These can be reckoned as generalizations of the trivial fat fbration of ℝ8 and the product of a line with the Harvey–Lawson coassociative fbration of ℝ7. The fbres will provide new examples of asymptotically conical Cayley submanifolds in the Bryant–Salamon manifolds of topology ℝ4, ℝ × S3 and Oℂℙ1 (−1).
| Type: | Article |
|---|---|
| Title: | Cayley fibrations in the Bryant–Salamon Spin(7) manifold |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10231-022-01273-z |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Spin(7) manifolds, Calibrated geometry, Cayley fbrations, Multi-moment map, Riemannian conifolds |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10180544 |
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