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
SN - 1073-2780
VL - 27
SP - 1565
EP - 1629
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 6
ER -