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arXiv · 1708.05253

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

Vestislav Apostolov·David M J Calderbank·Paul Gauduchon·Eveline Legendre
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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.

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Vestislav Apostolov, David M J Calderbank, Paul Gauduchon, Eveline Legendre. 2017-08-17. Levi-Kahler reduction of CR structures, products of spheres, and toric geometry. https://arxiv.org/abs/1708.05253

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