ON WEAK HOLONOMY

We prove that SU(n) (n ≥ 3) and Sp(n)U (1) (n ≥ 2) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases the manifold is Kähler.

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Bibliographic Details
Published in:Mathematica scandinavica 2005-01, Vol.96 (2), p.169-189
Main Author: ALEXANDROV, BOGDAN
Format: Article
Language:English
Subjects:
Cross products of vectors
Curvature
Group structure
Lie groups
Mathematical transitivity
Mathematical vectors
Parallel vectors
Product standards
Riemann manifold
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Summary:We prove that SU(n) (n ≥ 3) and Sp(n)U (1) (n ≥ 2) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases the manifold is Kähler.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-14951