Hodge theoretic results for nearly Kähler manifolds in all dimensions
Abstract
We generalize to nearly Kähler manifolds of arbitrary dimensions most of the Hodge-theoretic results for nearly Kähler 6-manifolds that were established by Verbitsky. In particular, for a compact nearly Kähler manifold of any dimension, the (appropriately defined) Hodge numbers are related to the Betti numbers in the same way as on a compact Kä manifold. In the 6-dimensional case, Verbitsky was able to say slightly more using the induced SU(3) structure. We discuss potential extensions of this to twistor spaces over positive scalar curvature quaternionic-Käl manifolds, which are a particular class of $(4n+2)$-dimensional nearly Kähler manifolds equipped with a special SU($n$) $\cdot$ U(1) structure.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Asian Journal of Mathematics
- Volume
- 30
- Issue
- 1
- Pages
- 115–131
- Publication date
- 1 January 2026
- Language
- EN