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

  title={Local Type III metrics with holonomy in \$\$\mathrm \{G\}_2^*\$\$G2∗},
  author={Christian Volkhausen},
  journal={Annals of Global Analysis and Geometry},
  • 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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