Transitive conformal holonomy groups

• Autorzy: Jesse Alt
• Języki publikacji: 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

EN

Conformal holonomy; Transitive group actions

Kategorie tematyczne

• 53A30: Conformal differential geometry
• 53C29: Issues of holonomy
• 53C30: Homogeneous manifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1710-1720

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Jesse Alt

• University of the Witwatersrand

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0009-7