Hermitian geometrically formal manifolds
Differential Geometry
2025-07-15 v1
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.
Cite
@article{arxiv.2507.10263,
title = {Hermitian geometrically formal manifolds},
author = {Tommaso Sferruzza and Adriano Tomassini},
journal= {arXiv preprint arXiv:2507.10263},
year = {2025}
}