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arXiv · 1711.10346

Homogeneous symplectic half-flat 6-manifolds

Fabio Podestà·Alberto Raffero
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Abstract

We consider 6-manifolds endowed with a symplectic half-flat SU(3)-structure and acted on by a transitive Lie group G of automorphisms. We review a classical result allowing to show the non-existence of compact non-flat examples. In the noncompact setting, we classify such manifolds under the assumption that G is semisimple. Moreover, in each case we describe all invariant symplectic half-flat SU(3)-structures up to isomorphism, showing that the Ricci tensor is always Hermitian with respect to the induced almost complex structure. This last condition is characterized in the general case.

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Fabio Podestà, Alberto Raffero. 2017-11-28. Homogeneous symplectic half-flat 6-manifolds. https://doi.org/10.1007/s10455-018-9615-3

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