Foscolo, L;
Haskins, M;
(2017)
New G₂-holonomy cones and exotic nearly Kahler structures on S⁶ and S³ x S³.
Annals of Mathematics
, 185
(1)
pp. 59-130.
10.4007/annals.2017.185.1.2.
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Abstract
There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G_{2}: the metric cone over a Riemannian 6-manifold M has holonomy contained in G_{2} if and only if M is a nearly Kaehler 6-manifold. A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kaehler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kaehler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kaehler structures in six dimensions.
Type: | Article |
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Title: | New G₂-holonomy cones and exotic nearly Kahler structures on S⁶ and S³ x S³ |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.4007/annals.2017.185.1.2 |
Publisher version: | http://dx.doi.org/10.4007/annals.2017.185.1.2 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
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.ucl.ac.uk/id/eprint/10082207 |
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