Hermitian geometrically formal manifolds

Tommaso Sferruzza; Adriano Tomassini

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arXiv · 2507.10263

Hermitian geometrically formal manifolds

Tommaso Sferruzza·Adriano Tomassini

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Abstract

We study Hermitian geometrically formal metrics on compact complex manifolds, focusing on Dolbeault, Bott-Chern, and Aeppli cohomologies. We establish topological and cohomological obstructions to their existence and we provide a detailed analysis for compact complex surfaces, complex parallelisable solvmanifolds, and Calabi-Eckmann manifolds. We prove that the standard blow-up metric on any blow-up of a K\"ahler manifold is not geometrically formal, and that K\"ahler metrics with nonnegative curvature operator are necessarily geometrically formal.

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Tommaso Sferruzza, Adriano Tomassini. 2025-07-14. Hermitian geometrically formal manifolds. https://arxiv.org/abs/2507.10263

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