New G2-holonomy cones and exotic nearly Kahler structures on S6 and S3 x S3

Journal Article (Journal Article)

There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 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 Kahler 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 Kahler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kahler 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 Kahler structures in six dimensions.

Full Text

Duke Authors

Cited Authors

  • Foscolo, L; Haskins, M

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 185 / 1

Start / End Page

  • 59 - 130

Electronic International Standard Serial Number (EISSN)

  • 1939-8980

International Standard Serial Number (ISSN)

  • 0003-486X

Digital Object Identifier (DOI)

  • 10.4007/annals.2017.185.1.2

Citation Source

  • Scopus