Hyperkähler ambient metrics associated with twistor CR manifolds

2023/09/06 by Marugame, Taiji
#32V05 (Primary) #53C26 (Secondary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.02778

Abstract

Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as ℙ¹-bundles over 3-dimensional conformal manifolds. In this paper, we embed a real analytic twistor CR manifold into the twistor space of the anti self-dual Poincaré-Einstein metric whose conformal infinity is the base conformal 3-manifold, and construct the associated Fefferman ambient metric as a neutral hyperkähler metric on the spinor bundle with the zero section removed. We also describe the structure of the Cheng--Yau type Kähler-Einstein metric which has the twistor CR manifold as the boundary at infinity.

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