Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II)

Abstract

Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G = SU2 × SU2, and \({M_{\rm reg} \subset M}\) its subset of regular points. We show that Mreg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly Kahler structures and that a 1-parameter subfamily of such structures smoothly extends over a singular orbit of type S3. This determines a new class of examples of nearly Kahler structures on T S3.