Communications in Analysis and Geometry

Volume 31 (2023)

Number 3

Deformation theory of nearly $G_2$ manifolds

Pages: 677 – 729

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n3.a5

Authors

Shubham Dwivedi (Department of Pure Mathematics, University of Waterloo, Ontario, Canada; and Institut für Mathematik, Humboldt-Universität zu Berlin, Germany)

Ragini Singhal (Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada; and Department of Mathematics, Université Libre de Bruxelles, Belgium)

Abstract

$\def\G{\mathrm{G}_2}$We study the deformation theory of nearly $\G$ manifolds. These are seven-dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\G$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\G$ structure on the Aloff–Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\G$ manifolds.

Full Text (PDF format)

Received 7 July 2020

Accepted 25 December 2020

Published 4 January 2024