An n-dimensional strictly pseudoconvex Hartogs domain DF can be equipped withanaturalKählermetricgF.Inthispaperweprovethatifm0gF isbalancedforagiven positive integer m0 then m0 > n and (DF , gF ) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.
Balanced metrics on Hartogs domains
LOI, ANDREA;ZEDDA, MICHELA
2011-01-01
Abstract
An n-dimensional strictly pseudoconvex Hartogs domain DF can be equipped withanaturalKählermetricgF.Inthispaperweprovethatifm0gF isbalancedforagiven positive integer m0 then m0 > n and (DF , gF ) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.
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