Levi-Kahler reduction of CR structures, products of spheres, and toric geometry

Vestislav Apostolov, David M J Calderbank, Paul Gauduchon, Eveline Legendre

Research output: Contribution to journalArticle

Abstract

We study CR geometry in arbitrary codimension, and introduce a process, which we call the Levi-Kahler quotient, for constructing Kahler metrics from CR structures with a transverse torus action. Most of the paper is devoted to the study of Levi-Kahler quotients of toric CR manifolds, and in particular, products of odd dimensional spheres. We obtain explicit descriptions and characterizations of such quotients, and find Levi-Kahler quotients of products of 3-spheres which are extremal in a weighted sense introduced by G. Maschler and the first author.
Original languageEnglish
Pages (from-to)1565-1629
Number of pages39
JournalMathematical Research Letters
Volume27
Issue number6
DOIs
Publication statusPublished - 2020

Keywords

  • math.DG
  • math.AG
  • 53C55, 53C25, 32Q15, 32V05, 14M25, 58J60

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