p-Kähler and balanced structures on nilmanifolds with nilpotent complex structures

2021/12/23 by Tommaso Sferruzza, Sferruzza, Tommaso, Nicoletta Tardini +1 · 4 citations
Mathematics · #22E25 #53C15 #53C25 #53C55 #Degeneracy (biology) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Invariant (physics) #Mathematical physics #Mathematics #Nilpotent #Pure mathematics #Sequence (biology) #math.DG #msc:22E25 #msc:53C15 #msc:53C25 #msc:53C55

paper · pdf · doi:10.48550/arxiv.2112.12418

published in arXiv (Cornell University) (Cornell University) · 11 pages

arxiv created 2021/12/23 · openalex publication_date 2021/12/23 · arxiv updated 2021/12/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/05

Abstract

Let (X,J) be a nilmanifold with a left-invariant nilpotent complex structure. We study the existence of p-Kähler structures (which include Kähler and balanced metrics) on X. More precisely, we determine an optimal p such that there are no p-Kähler structures on X. Finally, we show that, contrarily to the Kähler case, on compact complex manifolds there is no relation between the existence of balanced metrics and the degeneracy step of the Frölicher spectral sequence. More precisely, on balanced manifolds the degeneracy step can be arbitrarily large.

Cited by

• Complex structures on 2-step nilpotent Lie algebras arising from graphs
• Aeppli-Bott-Chern Massey products on non-Kähler solvmanifolds
• p-Kähler structures on nilmanifolds and holomorphically parallelizable manifolds
• p-Kähler structures on compact complex manifolds

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