Twisting Hermitian and hypercomplex geometries

Details Twisting Hermitian and hypercomplex geometries Twisting Hermitian and hypercomplex geometries

2008-12-15

arxiv.org/abs/0812.2780v1

Mathematics

Differential Geometry

27 pages

Scientific paper

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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