Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606647 | Differential Geometry and its Applications | 2007 | 11 Pages |
Abstract
We show that a 7-dimensional non-compact Ricci-flat Riemannian manifold with Riemannian holonomy G2 can admit non-integrable G2 structures of type RâS02(R7)âR7 in the sense of Fernández and Gray. This relies on the construction of some G2 solvmanifolds, whose Levi-Civita connection is known to give a parallel spinor, admitting a 2-parameter family of metric connections with non-zero skew-symmetric torsion that has parallel spinors as well. The family turns out to be a deformation of the Levi-Civita connection. This is in contrast with the case of compact scalar-flat Riemannian spin manifolds, where any metric connection with closed torsion admitting parallel spinors has to be torsion-free.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ilka Agricola, Simon G. Chiossi, Anna Fino,