We present several methods for the construction of balanced Hermitian structures on Lie groups. In our methods a partial differential equation is involved so that the resulting structures are in general non homogeneous. In particular, we prove that for 3-step nilpotent Lie groups G of dimension 6, any left-invariant complex structure on G admits a balanced Hermitianmetric. Starting from normal almost contact structures, we construct balanced metrics on 6-dimensional manifolds, generalizing warped products. Finally, explicit balanced Hermitian structures are also given on solvable Lie groups defined as semidirect products.

On balanced Hermitian structures on Lie groups / Medori, Costantino; Tomassini, Adriano; L., Ugarte. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 166:1(2013), pp. 233-250. [10.1007/s10711-012-9793-2]

On balanced Hermitian structures on Lie groups

MEDORI, Costantino;TOMASSINI, Adriano;
2013-01-01

Abstract

We present several methods for the construction of balanced Hermitian structures on Lie groups. In our methods a partial differential equation is involved so that the resulting structures are in general non homogeneous. In particular, we prove that for 3-step nilpotent Lie groups G of dimension 6, any left-invariant complex structure on G admits a balanced Hermitianmetric. Starting from normal almost contact structures, we construct balanced metrics on 6-dimensional manifolds, generalizing warped products. Finally, explicit balanced Hermitian structures are also given on solvable Lie groups defined as semidirect products.
On balanced Hermitian structures on Lie groups / Medori, Costantino; Tomassini, Adriano; L., Ugarte. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 166:1(2013), pp. 233-250. [10.1007/s10711-012-9793-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2525860
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