On the spaces of $(d+d^c)$-harmonic forms and $(d+d^Λ)$-harmonic forms on almost Hermitian manifolds and complex surfaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911258636189696 |
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| author | Sillari, Lorenzo Tomassini, Adriano |
| author_facet | Sillari, Lorenzo Tomassini, Adriano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10304 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the spaces of $(d+d^c)$-harmonic forms and $(d+d^Λ)$-harmonic forms on almost Hermitian manifolds and complex surfaces Sillari, Lorenzo Tomassini, Adriano Differential Geometry 32Q60, 53D15 (Primary) 53C15, 32J15 (Secondary) 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. |
| title | On the spaces of $(d+d^c)$-harmonic forms and $(d+d^Λ)$-harmonic forms on almost Hermitian manifolds and complex surfaces |
| topic | Differential Geometry 32Q60, 53D15 (Primary) 53C15, 32J15 (Secondary) |
| url | https://arxiv.org/abs/2310.10304 |