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arXiv · 2402.02537

Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds

Tommaso Sferruzza·Adriano Tomassini
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Abstract

We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is geometrically-Bott-Chern-formal. We also provide some partial results in higher dimensions for nilmanifolds endowed with a class of suitable complex structures. Furthermore, we prove that any Kähler solvmanifold is geometrically formal. Finally, we explicitly construct lattices for a complex solvable Lie group in the list of Nakamura [23] on which we provide a non vanishing quadruple $ABC$-Massey product.

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Tommaso Sferruzza, Adriano Tomassini. 2024-02-09. Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds. https://arxiv.org/abs/2402.02537

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