PCR-Kähler equivalent metrics in the Siegel domain

2023/04/17 by Kim, Joonhyung, Platis, Ioannis D., Sun, Li-Jie
#32C16 #53C17 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.08079

Abstract

Let \mathfrakH be the Heisenberg group. From the standard CR structure H of \mathfrakH we construct the complex hyperbolic structure of the Siegel domain. Additionally, using the same minimal data for \mathfrakH, that is, its Sasakian structure, we provide the Siegel domain with yet another Kähler structure: this structure is of unbounded negative sectional curvature, and its complex structure does not commute with the standard complex structure. However, we show that those two Kähler structures are \rm PCR Kähler equivalent, that is to say, essentially the same when restricted to H.

Related

• The Heisenberg group action on the Siegel domain and the structure of Bergman spaces
• Bergman representative coordinates on the Siegel-Jacobi disk
• Fine asymptotic geometry in the Heisenberg group
• Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
• Hölder-Topology of the Heisenberg group