# 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} }

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

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## Metrics with exceptional holonomy

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