Hodge decomposition theorem on compact $d$-Kähler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914834216386560 |
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| author | Amrutiya, Sanjay Jaiswal, Ayush |
| author_facet | Amrutiya, Sanjay Jaiswal, Ayush |
| contents | In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-Kähler manifold is a $d$-complex manifold equipped with a metric that satisfies a specific condition. We prove the Hodge decomposition theorem on compact $d$-Kähler manifolds, which establishes a crucial relationship between certain de-Rham cohomology groups and Dolbeault cohomology groups on a compact $d$-Kähler manifold . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hodge decomposition theorem on compact $d$-Kähler manifolds Amrutiya, Sanjay Jaiswal, Ayush Differential Geometry In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-Kähler manifold is a $d$-complex manifold equipped with a metric that satisfies a specific condition. We prove the Hodge decomposition theorem on compact $d$-Kähler manifolds, which establishes a crucial relationship between certain de-Rham cohomology groups and Dolbeault cohomology groups on a compact $d$-Kähler manifold . |
| title | Hodge decomposition theorem on compact $d$-Kähler manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.09312 |