2023/05/05 by Tommaso Sferruzza, Sferruzza, Tommaso · 2 citations
Mathematics · #32G05 (primary) 53B35 #53C55 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2305.03657
openalex publication_date 2023/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The property of admitting an astheno-Kähler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this paper, we prove necessary cohomological conditions for the existence of curves of astheno-Kähler metrics along curves of deformations starting from an initial compact complex manifold endowed with an astheno-Kähler metric. Furthermore, we apply our results providing obstructions to the existence of curves of astheno-Kähler metrics on two different families of real 8-dimensional nilmanifolds endowed with invariant nilpotent complex structures.