Deformation theory of nearly Kähler manifolds

Lorenzo Foscolo

doi:10.1112/jlms.12033

Deformation theory of nearly Kähler manifolds

Lorenzo Foscolo

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Abstract

Nearly Kähler manifolds are the Riemannian 6-manifolds admitting real Killing spinors. Equivalently, the Riemannian cone over a nearly Kähler manifold has holonomy contained in G2. In this paper we study the deformation theory of nearly Kähler manifolds, showing that it is obstructed in general. More precisely, we show that the infinitesimal deformations of the homogeneous nearly Kähler structure on the flag manifold are all obstructed to second order.

Original language	English
Pages (from-to)	586–612
Number of pages	27
Journal	Journal of the London Mathematical Society
Volume	95
Issue number	2
Early online date	8 Feb 2017
DOIs	https://doi.org/10.1112/jlms.12033
Publication status	Published - Apr 2017

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This is the peer reviewed version of the following article: Foscolo, L. (2017), Deformation theory of nearly Kähler manifolds. J. London Math. Soc., 95: 586–612, which has been published in final form at http://onlinelibrary.wiley.com/resolve/doi?DOI=10.1112/jlms.12033. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
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title = "Deformation theory of nearly K{\"a}hler manifolds",

abstract = "Nearly K{\"a}hler manifolds are the Riemannian 6-manifolds admitting real Killing spinors. Equivalently, the Riemannian cone over a nearly K{\"a}hler manifold has holonomy contained in G2. In this paper we study the deformation theory of nearly K{\"a}hler manifolds, showing that it is obstructed in general. More precisely, we show that the infinitesimal deformations of the homogeneous nearly K{\"a}hler structure on the flag manifold are all obstructed to second order.",

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Deformation theory of nearly Kähler manifolds

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