Deformations of G(2) and spin(7) structures

Journal article

We consider some 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 w 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 complexity of the Spin(7) case. © Canadian Mathematical Society 2005.

Authors: Karigiannis, S

• Publication status: Published
• Journal: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
• Volume: 57
• Issue: 5
• Pages: 1012-1055
• Publication date: 2005-10-01
• DOI: 10.4153/CJM-2005-039-x
• EISSN: 1496-4279
• ISSN: 0008-414X
• Language: English
• Keywords: Holonomy; Cross product; Metrics; G 2 Spin(7)