Locally conformal parallel $G_2$ and Spin(7) manifolds
TLDR
In this paper, the authors characterize compact locally conformal parallel fiber bundles over $S^1$ with compact nearly Kahler fiber for fiber bundles with fiber structures that are flat.Abstract:
We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly K\"ahler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is provided when the local parallel structures are flat.read more
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References
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Book
Spaces of Constant Curvature
TL;DR: In this article, a very concise treatment of riemannian and pseudo-riemannian manifolds and their curvatures is given, along with a discussion of the representation theory of finite groups.
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Real Killing spinors and holonomy
TL;DR: In this paper, the authors give a description of all complete simply connected Riemannian manifolds carrying real Killing spinors and present a construction method for manifolds with the exceptional holonomy groups G2 and Spin(7).
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Stable forms and special metrics
TL;DR: In this paper, the authors show how certain diffeomorphism-invariant functionals on differential forms in dimensions 6, 7 and 8 generate in a natural way special geometrical structures in these dimensions: metrics of holonomy G2 and Spin(7), metrics with weak holonomy SU(3) and G2, and a new and unexplored example in dimension 8.
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Riemannian manifolds with structure groupG2
M. Fernández,A. Gray +1 more
TL;DR: In this article, the covariant derivative of the fundamental 3-form of Riemannian manifolds with structure group G2 was studied. But the covariance of the derived 3-forms was not analyzed.
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Parallel spinors and connections with skew-symmetric torsion in string theory
Thomas Friedrich,Stefan Ivanov +1 more
TL;DR: In this article, all almost contact metric, almost hermitian and G2-structures admit a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection.