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Twisting Hermitian and hypercomplex geometries

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A twist construction for manifolds with torus action is described generalizing certain T-duality examples and constructions in hypercomplex geometry. It is applied to complex, SKT, hypercomplex, and HKT manifolds to construct compact simply connected examples. In particular, we find hypercomplex manifolds that admit no compatible HKT metric, and HKT manifolds whose Obata connection has holonomy contained in SL(n,H).

Original languageEnglish
JournalDuke Mathematical Journal
Volume155
Issue2
Pages (from-to)403-431
Number of pages29
ISSN0012-7094
DOIs
Publication statusPublished - 1 Nov 2010
Externally publishedYes

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