Local Type III metrics with holonomy in $$\mathrm {G}_2^*$$G2∗

@article{Volkhausen2018LocalTI,
title={Local Type III metrics with holonomy in \$\$\mathrm \{G\}_2^*\$\$G2∗},
author={Christian Volkhausen},
journal={Annals of Global Analysis and Geometry},
year={2018},
volume={56},
pages={113-136}
}
• Christian Volkhausen
• Published 2018
• Mathematics
• Annals of Global Analysis and Geometry
• Fino and Kath determined all possible holonomy groups of seven-dimensional pseudo-Riemannian manifolds contained in the exceptional, non-compact, simple Lie group $$\mathrm {G}_2^*$$G2∗ via the corresponding Lie algebras. They are distinguished by the dimension of their maximal semi-simple subrepresentation on the tangent space, the socle. An algebra is called of Type I, II or III if the socle has dimension 1, 2 or 3, respectively. This article proves that each possible holonomy group of Type… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-10 OF 27 REFERENCES

Local Type I Metrics with Holonomy in ${\rm G}_{2}^*$.

• Mathematics
• 2018
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Parallel tractor extension and ambient metrics of holonomy split G 2

• Mathematics
• 2011

Metrics with exceptional holonomy

VIEW 3 EXCERPTS

Torsion-free G*2(2)-structures with full holonomy on nilmanifolds

• Mathematics
• 2013
VIEW 1 EXCERPT

Holonomy groups of $G_2^*$-manifolds

• Mathematics
• 2016

Holonomy algebras of Einstein pseudo-Riemannian manifolds

VIEW 1 EXCERPT