Nearly Kahler metrics and torus symmetry

Giovanni Russo, Florida International University

Nearly Kahler manifolds are Riemannian spaces equipped with an almost Hermitian structure of special type. In dimension six, nearly Kahler metrics are Einstein with positive scalar curvature, and have interesting connections with G2 and spin geometry. At present there are very few compact examples, which are either homogeneous or of cohomogeneity one.

In this talk we explain a theory of nearly Kahler six-manifolds admitting a two-torus symmetry. The torus-action yields a multi-moment map, which we use as a Morse function to understand the structure of the whole manifold. In particular, we show how the local geometry of a nearly Kahler six-manifold can be recovered from three-dimensional data, and discuss connections with GKM theory.

QNC 2501