6-dimensional nearly Kaehler manifolds of cohomogeneity one

TL;DR

This paper classifies 6-dimensional strict nearly Kaehler manifolds with cohomogeneity one symmetry, showing they have constant sectional curvature if the symmetry group is simple, thus advancing understanding of their geometric structure.

Contribution

It provides a classification of compact 6-dimensional nearly Kaehler manifolds with cohomogeneity one symmetry and establishes curvature properties based on the symmetry group.

Findings

Classification of compact nearly Kaehler manifolds up to G-diffeomorphism.

Manifolds have constant sectional curvature when G is simple.

Advances understanding of symmetry and curvature in nearly Kaehler geometry.

Abstract

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant sectional curvature whenever the group G is simple.