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.

Homogeneous symplectic half-flat 6-manifolds

Raffero, Alberto
2019

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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https://link.springer.com/article/10.1007/s10455-018-9615-3
Hermitian Ricci tensor; Homogeneous spaces; Symplectic half-flat
Podestà, Fabio; Raffero, Alberto*
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1676268
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