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arXiv · 2102.01920

Pluriclosed and Strominger K\"ahler-like metrics compatible with abelian complex structures

Anna Fino·Nicoletta Tardini·Luigi Vezzoni
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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 K\"ahler-like condition.

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Anna Fino, Nicoletta Tardini, Luigi Vezzoni. 2021-02-03. Pluriclosed and Strominger K\"ahler-like metrics compatible with abelian complex structures. https://arxiv.org/abs/2102.01920

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