On Infinitesimal Holonomy and Isotropy Groups

Space-times and Holonomy Groups

This paper discusses the full holonomy group for space-time manifolds in Ein-stein's general relativity. Some applications of holonomy theory to Weyl manifolds are presented.

On the Infinitesimal Theory of Chow Groups

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Holonomy groups of Lorentzian manifolds

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker met...

Discrete Groups, Symmetric Spaces, and Global Holonomy

CONJUGATE SU(r)-CONNECTIONS AND HOLONOMY GROUPS

In this article we show that when the structure group of the reducible principal bundle P is SU(r) and Q ⊂ P is an SO(r)-subbundle of P , the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to [ r 2 ] , and use the estimate to show that for all odd prime r, if the holonomy group of the irreducible connection as above is simp...