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

Eveline Legendre (1) , Vestislav Apostolov (2) , David M J Calderbank , Paul Gauduchon (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CIRGET - Centre interuniversitaire de recherches en géométrie et topologie [Montréal]
3 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Domaines: Géométrie métrique [math.MG]; Géométrie algébrique [math.AG]

Eveline Legendre, Vestislav Apostolov, David M J Calderbank, Paul Gauduchon. Levi-Kahler reduction of CR structures, products of spheres, and toric geometry. 2018. ⟨hal-01881051⟩