2017/10/15 by Jesse Madnick, Madnick, Jesse
Mathematics · #53 Differential Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1710.05254
openalex publication_date 2017/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study nearly-Kahler 6-manifolds equipped with a cohomogeneity-two Lie group action for which the principal orbits are coisotropic. If the metric is complete, then we show that this last condition is automatically satisfied, and both the acting Lie group and the principal orbits are finite quotients of S3 × S1. We partition the class of such nearly-Kahler structures into three types (called I, II, III) and prove a local existence and generality result for each type. Metrics of Types I and II are shown to be incomplete. We also derive a quasilinear elliptic PDE system on the 2-dimensional orbit space which nearly-Kahler structures of Type I must satisfy. Finally, we remark on a relatively simple one-parameter family of Type III structures that turn out to be incomplete metrics that are cohomogeneity-one under the action of a larger group.