Hypercomplex structures associated to quaternionic manifolds

H. Pedersen*, Y. S. Poon, A. F. Swann

*Corresponding author af dette arbejde

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Abstract

If M is a quaternionic manifold and P is an S1-instanton over M, then Joyce constructed a hypercomplex manifold we call P(M) over M. These hypercomplex manifolds admit a U(2)-action of a special type permuting the complex structures. We show that up to double covers, all such hypercomplex manifolds arise in this way. Examples, including that of a hypercomplex structure on SU(3), show the necessity of including double covers of P(M).

OriginalsprogEngelsk
TidsskriftDifferential Geometry and its Application
Vol/bind9
Nummer3
Sider (fra-til)273-292
Antal sider20
ISSN0926-2245
DOI
StatusUdgivet - 1 jan. 1998
Udgivet eksterntJa

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