Nearly Kahler homogeneous manifolds with positive curvature

TL;DR

This paper classifies 2n-dimensional compact homogeneous nearly Kahler manifolds with positive sectional curvature, showing they are isometric to well-known symmetric spaces or spheres, thus confirming a conjecture by Gray.

Contribution

It proves that such manifolds are isometric to specific symmetric spaces or spheres, providing a complete classification under the given conditions.

Findings

Identifies CP^{n} with Fubini-Study metric as a nearly Kahler manifold with positive curvature

Shows S^{6} with constant curvature fits the classification

Confirms Gray's conjecture for these manifolds

Abstract

We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CP^{n}, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n =2m-1, or to S^{6} as Riemannian manifold with constant sectional curvature. This is a positive answer for a revised version of a conjecture given by Gray.