The adapted hyper-Kähler structure on the crown domain

2017/11/05 by Laura Geatti, Geatti, Laura, Andrea Iannuzzi +1
Mathematics · #32M15 #37J15 #53C26 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32M15 #msc:37J15 #msc:53C26

paper · pdf · doi:10.48550/arxiv.1711.01605

arxiv created 2017/11/05 · arxiv updated 2017/11/07

Abstract

Let Ξ be the crown domain associated with a non-compact irreducible hermitian symmetric space G/K. We give an explicit description of the unique G-invariant adapted hyper-Kähler structure on Ξ, i. e. compatible with the adapted complex structure J_ad and with the G-invariant Kähler structure of G/K. We also compute invariant potentials of the involved Kähler metrics and the associated moment maps.

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