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2012 | 10 | 5 | 1710-1720
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Transitive conformal holonomy groups

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EN
Abstrakty
EN
For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly on ℝp+1,q+1. For the rest, we show that they must be compact and act decomposably on ℝp+1,q+1, in particular, by known facts about conformal holonomy the conformal class [g] must contain a metric which is either Einstein (if p = 0 or q = 0) or locally isometric to a so-called special Einstein product.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
5
Strony
1710-1720
Opis fizyczny
Daty
wydano
2012-10-01
online
2012-07-24
Twórcy
autor
Bibliografia
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  • [24] Leitner F., A remark on unitary conformal holonomy, In: Symmetries and Overdetermined Systems of Partial Differential Equations, Minneapolis, July 17-August 4, 2006, IMA Vol. Math. Appl., 144, Springer, New York, 2008, 445–460 http://dx.doi.org/10.1007/978-0-387-73831-4_23
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0009-7
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