## Abstract

There is a rich theory of so-called (strict) nearly Kähler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kähler 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 G2: the metric cone over a Riemannian 6-manifold M has holonomy contained in G2 if and only if M is a nearly Kähler 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 Kähler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kähler 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 Kähler structures in six dimensions.

Original language | English |
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Pages (from-to) | 59-130 |

Journal | Annals of Mathematics |

Volume | 185 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2 Dec 2016 |

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