2017/08/17 by Vestislav Apostolov, David M. J. Calderbank, Apostolov, Vestislav +5
Mathematics · #14M25 #32Q15 #32V05 #53C25 #53C55 #58J60 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · doi:10.48550/arxiv.1708.05253
openalex publication_date 2017/08/17 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
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.