Jean-Baptiste Butruille
Published 2006-12-21Version 1
We classify six-dimensional homogeneous nearly K\"{a}hler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly K\"{a}hler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are $S^3 \times S^3$, the complex projective space $\CM P^3$, the flag manifold $\mathbb F^3$ and the sphere $S^6$. We develop, about each of these spaces, a distinct aspect of nearly K\"{a}hler geometry and make in the same time a sharp description of its specific homogeneous structure.
Comments: This is the english version of an older article written in french (Classification des vari\'{e}t\'{e}s approximativement k\"{a}hleriennes homog\`{e}nes, Ann. Global Anal. Geom. 27, 201-225, 2005). It contains no new results. However, we modified the structure of the paper, simplified some proofs and added a lot of explanations, especially on 3-symmetric spaces. It can be read as a sort of survey on nearly K\"{a}hler manifolds
The twisted Spin$^c$ Dirac operator on Kähler submanifolds of the complex projective space
New characterizations of ruled real hypersurfaces in complex projective space
Almost Hermitian structures on tangent bundles
![QR code for arXiv:math/0612655 [math.DG]](http://oss.arxitics.com/images/favicon.svg)