New G<inf>2</inf>-holonomy cones and exotic nearly Kahler structures on S<sup>6</sup> and S<sup>3</sup> x S<sup>3</sup>

Loading...
Thumbnail Image

Date

2017-01-01

Journal Title

Journal ISSN

Volume Title

Repository Usage Stats

84
views
49
downloads

Citation Stats

Abstract

© 2017 Department of Mathematics, Princeton University. 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.

Department

Description

Provenance

Citation

Published Version (Please cite this version)

10.4007/annals.2017.185.1.2

Publication Info

Foscolo, L, and M Haskins (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 Retrieved from https://hdl.handle.net/10161/19606.

This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.


Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.