Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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pp: 399–423

DOI: 10.4171/079-1/11

Homogeneous nearly Kähler manifolds

Jean-Baptiste Butruille[1]

(1) Université de Cergy-Pontoise, France

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 ℂP3, the flag manifold

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