Deformations of G_2 and Spin(7) Structures on Manifolds

Abstract

We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross product. We present a system of partial differential equations for an unknown vector field whose solution would yield a manifold with holonomy G_2. Similarly we consider analogous constructions for Spin(7) structures on 8-manifolds. Some of the results carry over directly, while others do not because of the increased non-linearity of the Spin(7) case.

51 pages, no figures, part of author's Ph.D. Thesis. Version 4: Changes made after publication: There were sign errors in equations (2.26) and (2.34) and in the proof of Lemma 2.4.3 that have now been corrected in this arXiv version. Also Remark 3.3.7 was incorrect and has been removed. Finally, hyperlinks now added

References in corpus (2)

• The geometry of three-forms in six and seven dimensions
• Duality and Fibrations on G_2 Manifolds

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