TY - JOUR

T1 - Levi-Kahler reduction of CR structures, products of spheres, and toric geometry

AU - Apostolov, Vestislav

AU - Calderbank, David M J

AU - Gauduchon, Paul

AU - Legendre, Eveline

N1 - Related to arXiv:1708.04942

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - math.DG

KW - math.AG

KW - 53C55, 53C25, 32Q15, 32V05, 14M25, 58J60

U2 - 10.4310/MRL.2020.V27.N6.A1

DO - 10.4310/MRL.2020.V27.N6.A1

M3 - Article

VL - 27

SP - 1565

EP - 1629

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 6

ER -