Year: 2025
Type: preprint
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 Kähler manifold is not geometrically formal, and that Kähler metrics with nonnegative curvature operator are necessarily geometrically formal.
Source: arXiv (Cornell University)
Authors: Sferruzza, Tommaso, Tomassini, Adriano
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891878029
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