Geodesic
Deformations of G 2 and Spin(7) Structures
Canadian journal of mathematics, Tome 57 (2005) no. 5, pp. 1012-1055

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2005-039-x
Mots-clés : 53C26, 53C29, G2 Spin(7), holonomy, metrics, cross product 
Karigiannis, Spiro. Deformations of G 2 and Spin(7) Structures. Canadian journal of mathematics, Tome 57 (2005) no. 5, pp. 1012-1055. doi: 10.4153/CJM-2005-039-x
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