Locally conformal Kähler reduction
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Rosa Gini
Abstract
We define reduction of locally conformal Kähler manifolds, considered as conformal Hermitian manifolds, and we show its equivalence with an unpublished construction given by Biquard and Gauduchon. We give two independent, equivalent definitions, the first via local charts, the second via lifting to Kähler reduction of the universal covering. By a recent result of Kamishima and the second author, in the Vaisman case (that is, when a metric in the conformal class has parallel Lee form) if the manifold is compact its universal covering comes equipped with the structure of Kähler cone over a Sasaki compact manifold. We show the compatibility between our reduction and Sasaki reduction, hence describing a subgroup of automorphisms whose action causes the quotient to bear a Vaisman structure. Then we apply this theory to construct a wide class of Vaisman manifolds.
© Walter de Gruyter
Articles in the same Issue
- Locally conformal Kähler reduction
- A finiteness theorem for representability of quadratic forms by forms
- On braided tensor categories of type BCD
- Equivariant vector bundles on group completions
- On the Galois group of 2-extensions with restricted ramification
- Gaussian maps, Gieseker-Petri loci and large theta-characteristics
- Approximation and the n-Berezin transform of operators on the Bergman space
- Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
Articles in the same Issue
- Locally conformal Kähler reduction
- A finiteness theorem for representability of quadratic forms by forms
- On braided tensor categories of type BCD
- Equivariant vector bundles on group completions
- On the Galois group of 2-extensions with restricted ramification
- Gaussian maps, Gieseker-Petri loci and large theta-characteristics
- Approximation and the n-Berezin transform of operators on the Bergman space
- Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
