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Homogeneous symplectic half-flat 6-manifolds

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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 of Wolf and Gray allowing one to show the nonexistence 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 property of the Ricci tensor is characterized in the general case.

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Acknowledgements

The authors would like to thank Anna Fino for useful comments as well as the anonymous referee for his/her valuable remarks and suggestions.

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  1. Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134, Florence, Italy

    Fabio Podestà & Alberto Raffero

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  1. Fabio Podestà
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  2. Alberto Raffero
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Correspondence to Alberto Raffero.

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The authors were supported by GNSAGA of INdAM.

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Podestà, F., Raffero, A. Homogeneous symplectic half-flat 6-manifolds. Ann Glob Anal Geom 55, 1–15 (2019). https://doi.org/10.1007/s10455-018-9615-3

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