On the spaces of (d+d^c)-harmonic forms and (d+d^Λ)-harmonic forms on almost Hermitian manifolds and complex surfaces

2023/10/16 by Lorenzo Sillari, Sillari, Lorenzo, Адриано Томассини +1 · 1 citation
Mathematics · #32J15 (Secondary) #32Q60 #53D15 (Primary) 53C15 #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.2310.10304

openalex publication_date 2023/10/16 · openalex created_date 2023/10/18 · openalex updated_date 2026/07/28

Abstract

We study the spaces of (d + d^c)-harmonic forms and (d + d^Λ)-harmonic forms, the natural generalization of the spaces of Bott-Chern harmonic forms, resp. symplectic harmonic forms from complex, resp. symplectic, manifolds to almost Hermitian manifolds. With the same techniques, we also prove that Bott-Chern and Aeppli numbers of compact complex surfaces depend only on the topology of the underlying manifold, a fact that was well-known for Hodge numbers of compact complex surfaces. We give several applications to compact quotients of Lie groups by a lattice.

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• Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds

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