∂∂-Lemma and p-Kähler structures on families of solvmanifolds

2024/03/15 by Andrea Cattaneo, Cattaneo, Andrea, Адриано Томассини +1 · 1 citation
Mathematics · #32J27 #32Q99 #57T15 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2403.10126

openalex publication_date 2024/03/15 · openalex created_date 2024/03/19 · openalex updated_date 2026/07/28

Abstract

We provide families of compact (n + 1)-dimensional complex non Kähler manifolds satisfying the ∂∂-Lemma, with holomoprhically trivial canonical bundle, carrying a balanced metric and with no p-Kähler structures. Such a construction extends to the completely solvable case in any dimension Nakamura's construction of low-dimensional holomorphically parallelizable solvmanifolds.

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• Aeppli-Bott-Chern Massey products on non-Kähler solvmanifolds

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