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- Title
Local Type III metrics with holonomy in G2∗.
- Authors
Volkhausen, Christian
- Abstract
Fino and Kath determined all possible holonomy groups of seven-dimensional pseudo-Riemannian manifolds contained in the exceptional, non-compact, simple Lie group G 2 ∗ 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 III can indeed be realized by a metric of signature (4, 3). For this purpose, metrics are explicitly constructed, using Cartan's methods of exterior differential systems, such that the holonomy of the manifold has the desired properties.
- Subjects
HOLONOMY groups; EXTERIOR differential systems; LIE algebras; LIE groups; ALGEBRA; MANIFOLDS (Mathematics)
- Publication
Annals of Global Analysis & Geometry, 2019, Vol 56, Issue 1, p113
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-019-09659-8