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arXiv · 0812.2780

Twisting Hermitian and hypercomplex geometries

Andrew Swann
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Abstract

A twist construction for manifolds with torus action is described generalising 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 $SL(n,\mathbb H)$.

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Andrew Swann. 2008-12-15. Twisting Hermitian and hypercomplex geometries. https://doi.org/10.1215/00127094-2010-059

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