On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908872550121472 |
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| author | Tan, Qiang Wang, Hongyu Wang, Ken Zhang, Zuyi |
| author_facet | Tan, Qiang Wang, Hongyu Wang, Ken Zhang, Zuyi |
| contents | In this paper, we introduce $\mathcal{D}^+_J$, a generalization of $\partial\bar{\partial}$ operator on higher dimensional almost Kähler manifolds. Using the $\mathcal{D}^+_J$ operator, we investigate the $\bar{\partial}$-problem in almost Kähler geometry and explore the generalized Monge-Ampère equation on almost Kähler manifolds. We establish a uniqueness up to the addition of a constant and local existence theorem for this equation. At last, we find an elliptical system for $\mathcal{D}^+_J$ operator. As an application, we reorganize the result of Tosatti-Weinkove-Yau in \cite{TWY}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds Tan, Qiang Wang, Hongyu Wang, Ken Zhang, Zuyi Differential Geometry In this paper, we introduce $\mathcal{D}^+_J$, a generalization of $\partial\bar{\partial}$ operator on higher dimensional almost Kähler manifolds. Using the $\mathcal{D}^+_J$ operator, we investigate the $\bar{\partial}$-problem in almost Kähler geometry and explore the generalized Monge-Ampère equation on almost Kähler manifolds. We establish a uniqueness up to the addition of a constant and local existence theorem for this equation. At last, we find an elliptical system for $\mathcal{D}^+_J$ operator. As an application, we reorganize the result of Tosatti-Weinkove-Yau in \cite{TWY}. |
| title | On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.14101 |