Classification des variété approximativement kähleriennes homogénes
By Jean-Baptiste Butruille. 2004
135 citations recorded by the source corpus.
A Riemannian homogeneous manifold admitting a strict nearly-Kähler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions. The six-dimensional homogeneous spaces, S3 × S3, S6, CP(3) and the flag manifold F(1, 2) have a unique (after a change of scale) nearly-Kähler, invariant structure. For the first one we solve a differential equation on the SU(3)-structure given by Reyes Carrión. For the last two it is obtained by canonical variation of the Kähler structure of the twistor space over a four-dimensional manifold. Finally, from Bär, a nearly-Kähler structure on the sphere S6 corresponds to a constant 3-form on the Riemannian cone R7.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8301dc6238cd09e8b2442923ecf1cdc56d194766
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In Applied Mathematics
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Citations in the corpus
- Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II) (2009, background): “Actually, Butruille proved that these space exhaust the class of homogeneous strict NK manifolds in six dimensions ([3]).”
- Homogeneous nearly K\"{a}hler manifolds (2006, methodology): “We could adapt Muskarov’s proof [34] for this case, as was done in [8], calculating ∇J for all g with Levi-Civita connection ∇ in the 3-dimensional space of invariants metrics, and all invariant almost complex structure J , or we can look more carefully at the structure of F(3), as we will do now.”