Geometriae Dedicata

, Volume 123, Issue 1, pp 73–78 | Cite as

Regular quantizations and covering maps

  • Andrea Loi
Original Paper


Let \(\tilde{M} \rightarrow M\) be a holomorphic (unbranched) covering map between two compact complex manifolds, with \(b_{2}(\tilde{M})=1\). We prove that if \(\tilde{M}\) and M both admit regular Kähler forms \(\tilde\omega\) and ω respectively then, up to homotheties, \((\tilde{M}, \tilde\omega)\) and (M, ω) are biholomorphically isometric.


Kähler metrics Constant scalar curvature metrics Diastasis Quantum mechanics 

Mathematics Subject Classifications (2000)

53C55 58F06 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di CagliariCagliariItaly

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