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arXiv · 2310.10304

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

Lorenzo Sillari·Adriano Tomassini
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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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Lorenzo Sillari, Adriano Tomassini. 2023-12-19. On the spaces of $(d+d^c)$-harmonic forms and $(d+d^Λ)$-harmonic forms on almost Hermitian manifolds and complex surfaces. https://doi.org/10.4171/rmi%2F1492

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