Homogeneous nearly Kähler manifolds

2006/12/21 by Butruille, Jean-Baptiste
#53C10 #53C15 #53C25 #53C28 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0612655

Abstract

We classify six-dimensional homogeneous nearly Kähler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly Kähler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are S³ × S³, the complex projective space \CM P³, the flag manifold \mathbb F³ and the sphere S⁶. We develop, about each of these spaces, a distinct aspect of nearly Kähler geometry and make in the same time a sharp description of its specific homogeneous structure.

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• Homogeneous nearly Kähler manifolds
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• Nearly Kahler homogeneous manifolds with positive curvature