We show that the existence of a left-invariant pluriclosed Hermitian metric on a unimodular Lie group with a left-invariant abelian complex structure forces the group to be 2-step nilpotent. Moreover, we prove that the pluriclosed flow starting from a left-invariant Hermitian metric on a 2-step nilpotent Lie group preserves the Strominger Kahler-like condition.

Pluriclosed and Strominger Kähler–like metrics compatible with abelian complex structures / Fino, A.; Tardini, N.; Vezzoni, L.. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - (2022). [10.1112/blms.12661]

Pluriclosed and Strominger Kähler–like metrics compatible with abelian complex structures

Fino A.;Tardini N.;
2022-01-01

Abstract

We show that the existence of a left-invariant pluriclosed Hermitian metric on a unimodular Lie group with a left-invariant abelian complex structure forces the group to be 2-step nilpotent. Moreover, we prove that the pluriclosed flow starting from a left-invariant Hermitian metric on a 2-step nilpotent Lie group preserves the Strominger Kahler-like condition.
Pluriclosed and Strominger Kähler–like metrics compatible with abelian complex structures / Fino, A.; Tardini, N.; Vezzoni, L.. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - (2022). [10.1112/blms.12661]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2929895
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