-quotient of -structures
arXiv:1909.03962 · doi:10.1007/s10455-020-09710-z
Abstract
If a manifold admits a free action preserving the fundamental -form then the quotient space is naturally endowed with a -structure. We derive equations relating the intrinsic torsion of the -structure to that of the -structure together with the additional data of a Higgs field and the curvature of the -bundle; this can be interpreted as a Gibbons-Hawking-type ansatz for -structures. We focus on the three torsion classes: torsion-free, locally conformally parallel and balanced. In particular we show that if is a manifold then cannot have holonomy contained in unless is in fact a Calabi-Yau -fold and is the product of a Calabi-Yau -fold and an interval. We also derive a new formula for the Ricci curvature of -structures in terms of the torsion forms. We then describe this -quotient construction in detail for the Bryant-Salamon metric on the spinor bundle of and for the flat metric on .
arXiv commentTo appear in Annals of Global Analysis and Geometry. Minor changes following the referee's comments
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